Geometry worksheet on rotations and reflections on the coordinate plane, featuring nine exercises with shapes A and B on grids.

Let me work through each problem carefully by analyzing the coordinates of shapes A and B to determine the transformation.

Problem 1:
Shape A (orange triangle): vertices at approximately (-4,1), (-2,1), (-2,5)
Shape B (teal triangle): vertices at approximately (2,1), (4,1), (2,5)

Looking at this: A is on the left side, B is on the right side. They appear to be mirror images across the y-axis (x=0).
- (-4,1) → (4,1)? No wait, let me look again.
- Actually looking more carefully: A has vertices at (-4,1), (-2,1), (-2,5)
- B has vertices at (2,1), (4,1), (2,5)

Wait, if it's reflection in y-axis: (-4,1)→(4,1), (-2,1)→(2,1), (-2,5)→(2,5)
That would give B vertices at (4,1), (2,1), (2,5) - which matches!

So Problem 1: Reflection in the y-axis (or line x=0)

Problem 2:
Shape A (orange triangle): vertices at approximately (-4,1), (-2,1), (-2,5)
Shape B (teal triangle): vertices at approximately (1,2), (5,2), (1,4)

A is upright triangle, B appears rotated. Let me check rotation 90° clockwise about origin:
(-4,1) → (1,4) ✓
(-2,1) → (1,2) ✓
(-2,5) → (5,2) ✓

Yes! Rotation 90° clockwise about the origin (0,0).

Problem 3:
Shape A (orange triangle): vertices at approximately (-4,-5), (-2,-5), (-2,-1)
Shape B (teal triangle): vertices at approximately (-4,5), (-2,5), (-2,1)

A is below x-axis, B is above. They look like reflections across x-axis.
(-4,-5) → (-4,5) ✓
(-2,-5) → (-2,5) ✓
(-2,-1) → (-2,1) ✓

Reflection in the x-axis (or line y=0).

Problem 4:
Shape A (orange trapezoid): vertices at approximately (2,-3), (5,-3), (5,-4), (3,-4)... let me look more carefully.
Actually A appears to be at roughly (2,-2) to (5,-4) area.
Shape B (teal trapezoid): appears to be at (-5,-2) to (-2,-4) area.

These look like reflections across the y-axis.
If A is at (2,-2), (5,-2), (5,-4), (3,-4)... wait let me reconsider.

Looking at the image more carefully for problem 4:
- A (orange) appears to be a trapezoid on the right side, around x=2 to x=5, y=-2 to y=-4
- B (teal) appears to be a trapezoid on the left side, around x=-5 to x=-2, y=-2 to y=-4

Reflection in y-axis: (x,y) → (-x,y)
If A has vertices (2,-2), (5,-2), (5,-4), (3,-4)
Then B would have (-2,-2), (-5,-2), (-5,-4), (-3,-4)

Hmm, but looking at B it seems to span from about x=-5 to x=-2. Let me reconsider A's position.

Actually looking again, A might be at (2,-2), (5,-2), (5,-4), (3,-4) - that's a trapezoid with top wider than bottom... no wait.

Let me think differently. The shapes look like they could be related by reflection in y-axis. Both are at similar y-levels but opposite x sides.

Reflection in the y-axis (line x=0).

Problem 5:
Shape A (orange trapezoid): upper left area, around x=-4 to x=-2, y=1 to y=3
Shape B (teal trapezoid): lower right area, around x=1 to x=4, y=-1 to y=-3

This looks like rotation 180° about origin.
If A has vertices (-4,1), (-2,1), (-2,3), (-4,3)...
Rotation 180°: (x,y) → (-x,-y)
(-4,1) → (4,-1)
(-2,1) → (2,-1)
(-2,3) → (2,-3)
(-4,3) → (4,-3)

That would put B at x=2 to x=4, y=-1 to y=-3. That seems to match!

Rotation 180° about the origin.

Problem 6:
Shape A (orange trapezoid): lower area, around x=-4 to x=-2, y=-4 to y=-6
Shape B (teal trapezoid): upper area, around x=-4 to x=-2, y=2 to y=4

Both on the same x-side but different y. This looks like reflection in a horizontal line.
If A is at y=-4 to y=-6 and B is at y=2 to y=4...
The midpoint between corresponding points: if A vertex at y=-5 maps to B vertex at y=3, midpoint is y=-1.
Or if A at y=-4 maps to B at y=2, midpoint is y=-1.

Reflection in the line y=-1.

Wait, let me reconsider. Looking at the positions:
- A appears centered around y=-5
- B appears centered around y=3
Midpoint: (-5+3)/2 = -1

So reflection in line y=-1.

Actually, let me look again. A might be at y=-4 to y=-6 (center y=-5), B at y=2 to y=4 (center y=3). Midpoint = -1. Yes, reflection in y=-1.

Hmm, but actually looking more carefully at problem 6, both shapes seem to be at similar x positions (around x=-4 to x=-2). So it's a vertical reflection.

Reflection in the line y=-1.

Problem 7:
Shape A (orange L-shape): lower right area, around x=1 to x=3, y=-1 to y=-3
Shape B (teal L-shape): upper left area, around x=-4 to x=-2, y=2 to y=4

This looks like rotation 180° about some point, or reflection.

Let me check rotation 180° about origin:
If A has vertices... let's say (1,-1), (3,-1), (3,-3), (2,-3), (2,-2), (1,-2)
Rotation 180°: (-1,1), (-3,1), (-3,3), (-2,3), (-2,2), (-1,2)

That would put B at x=-3 to x=-1, y=1 to y=3. Close to what I see.

Actually looking at B, it seems to be at x=-4 to x=-2, y=2 to y=4. Let me reconsider A's position.

If A is at (1,-2), (3,-2), (3,-4)... no wait.

Let me try: A at approximately (1,-1) to (3,-3), B at (-4,2) to (-2,4).

For rotation 180° about point (h,k): (x,y) → (2h-x, 2k-y)
If (1,-1) → (-4,4)? Then 2h-1=-4, so h=-1.5; 2k-(-1)=4, so k=1.5
Check (3,-3) → (-2,6)? 2(-1.5)-3=-6, not -2. Doesn't work.

Let me try reflection. If it's reflection in some line...

Actually, let me reconsider the positions. Looking at problem 7:
- A (orange) is an L-shape in the lower right quadrant
- B (teal) is an L-shape in the upper left quadrant

They look like they could be related by rotation 180° about the origin, or reflection in y=-x line, or some combination.

Let me try rotation 180° about origin more carefully:
If A vertices are approximately (1,-1), (3,-1), (3,-2), (2,-2), (2,-3), (1,-3)
After 180° rotation: (-1,1), (-3,1), (-3,2), (-2,2), (-2,3), (-1,3)

That gives B at x=-3 to x=-1, y=1 to y=3.

But B appears to be at x=-4 to x=-2, y=2 to y=4 based on my initial reading. Let me re-examine.

Actually, I think I may have misread the positions. Let me assume rotation 180° about origin is correct since the shapes are in opposite quadrants and appear to be the same orientation (just flipped).

Rotation 180° about the origin.

Problem 8:
Shape A (orange L-shape): lower area, around x=1 to x=3, y=-2 to y=-5
Shape B (teal L-shape): upper left area, around x=-4 to x=-3, y=2 to y=5

Hmm, these don't look like simple rotations or reflections about origin/axes.

Let me think... A is in lower right, B is in upper left.

If rotation 90° counterclockwise about origin: (x,y) → (-y,x)
If A has vertex at (2,-3), after rotation: (3,2)
If A has vertex at (3,-2), after rotation: (2,3)

That could work! Let me check more carefully.

Actually, looking at the shapes:
- A appears to be an L-shape pointing down-right
- B appears to be an L-shape pointing up-left

Rotation 90° counterclockwise about origin seems plausible.

Let me verify: If A vertices are (1,-2), (3,-2), (3,-5), (2,-5), (2,-3), (1,-3)
After 90° CCW: (2,1), (2,3), (5,3), (5,2), (3,2), (3,1)

That puts B at x=2 to x=5, y=1 to y=3. But B appears to be at x=-4 to x=-3, y=2 to y=5.

Hmm, that doesn't match. Let me reconsider.

Maybe it's rotation 90° clockwise? (x,y) → (y,-x)
(1,-2) → (-2,-1)
(3,-2) → (-2,-3)
That puts things in lower left, not upper left.

What about reflection in y=-x? (x,y) → (-y,-x)
(1,-2) → (2,-1)
(3,-2) → (2,-3)
Still lower right area.

Let me try rotation 180° about some point other than origin.

Actually, let me reconsider the positions. Maybe I'm misreading the grid.

Looking at problem 8 again:
- A (orange) appears to be at roughly x=1 to x=3, y=-2 to y=-5 (lower right)
- B (teal) appears to be at roughly x=-4 to x=-3, y=2 to y=5 (upper left)

For these to be related by a single transformation...

Rotation 90° counterclockwise about origin:
Point (2,-3) → (3,2)
Point (3,-2) → (2,3)

If A is centered around (2,-3.5) and B is centered around (-3.5,3.5)...

Hmm, let me try: if A has a "corner" at (2,-2) and B has corresponding corner at (-2,2)... that would be reflection in y=-x line? No, (2,-2) reflected in y=-x gives (2,-2)→(2,-2)... wait.

Reflection in y=-x: (x,y) → (-y,-x)
(2,-2) → (2,-2) - that's on the line itself.

Let me try rotation 90° CCW about origin again with different A coordinates.

If A is at (1,-2), (2,-2), (2,-5), (1,-5)... that's a rectangle, not L-shape.

OK let me just look at this differently. The L-shapes:
- A: looks like it has a vertical part going down and a horizontal part going right
- B: looks like it has a vertical part going up and a horizontal part going left

This suggests rotation 180° about some point, or possibly reflection.

Actually, rotation 180° about origin:
If A vertex at (2,-3) → (-2,3)
If A vertex at (3,-2) → (-3,2)

That could place B in the upper left! Let me check if this works.

If A is approximately at x=1 to x=3, y=-2 to y=-5:
After 180° rotation: x=-3 to x=-1, y=2 to y=5

B appears to be at x=-4 to x=-3, y=2 to y=5. Close but x-range is slightly off.

I think rotation 180° about the origin is the answer for problem 8.

Wait, but problem 7 also seemed like 180° rotation. Let me reconsider problem 7.

Problem 7:
- A at lower right (x positive, y negative)
- B at upper left (x negative, y positive)

If both are 180° rotations about origin, that makes sense.

Actually, let me reconsider problem 8. The shapes might be related by a different transformation.

Looking more carefully: A is an L-shape in lower right, B is an L-shape in upper left but oriented differently.

If A is like ┘ shape (bottom-right corner) and B is like ┌ shape (top-left corner), then rotation 180° would convert ┘ to ┌. Yes!

So problem 8: Rotation 180° about the origin.

Hmm but then problems 7 and 8 would both be 180° rotation. Let me reconsider problem 7.

Problem 7: A and B both appear to be L-shapes. If A is ┘ and B is └ (mirror), then it's reflection. If A is ┘ and B is ┌ (rotated 180°), then it's rotation.

Looking at the image description again... I need to be more careful.

Let me just go with my best analysis:

Problem 7: Rotation 180° about origin (shapes in opposite quadrants, same orientation when rotated)
Problem 8: Could be rotation 90° CCW or 180° depending on exact orientation

Actually, let me reconsider problem 8 once more. If A is at (1,-2) to (3,-5) area and B is at (-4,2) to (-3,5) area...

For rotation 90° CCW about origin: (x,y) → (-y,x)
(1,-2) → (2,1)
(3,-5) → (5,3)
That gives x=2 to x=5, y=1 to y=3. Not matching B's position.

For rotation 180° about origin: (x,y) → (-x,-y)
(1,-2) → (-1,2)
(3,-5) → (-3,5)
That gives x=-3 to x=-1, y=2 to y=5. Closer to B's position!

I'll go with rotation 180° about origin for problem 8.

Problem 9:
Shape A (orange house/pentagon): upper right area, around x=2 to x=4, y=3 to y=6
Shape B (teal pentagon): lower left area, around x=-4 to x=-2, y=-1 to y=-3

A is a house shape pointing up, B appears to be pointing left (rotated).

If rotation 90° counterclockwise about origin:
House pointing up at (2-4, 3-6) → would point left at (-6 to -3, 2 to 4)...

Hmm, let me think. If A is a house with peak at top, after 90° CCW rotation, peak would point left.

If A vertices include (3,6) [peak], after 90° CCW: (-6,3)
If A has base at y=3, after rotation: x=-3

So B would have peak at (-6,3) and base around x=-3. That's in upper left, not lower left.

What about rotation 90° clockwise? (x,y) → (y,-x)
(3,6) → (6,-3)
Base at y=3 → x=3, so base at x=3, y varies...

Hmm, that puts peak at (6,-3) which is lower right.

What about rotation 180°? (x,y) → (-x,-y)
(3,6) → (-3,-6)
Base at y=3 → y=-3
So peak at (-3,-6) and base at y=-3. Peak pointing down.

But B appears to have peak pointing left based on the shape description.

Let me reconsider. If B is a pentagon/house shape pointing left, and A is pointing up...

Rotation 90° counterclockwise: up → left ✓
But the position doesn't seem to match origin rotation.

Maybe it's rotation 90° CCW about a different point?

Or maybe I'm misreading B's orientation. Let me assume B is pointing left (peak on left side).

If rotation 90° CCW about origin doesn't give the right position, maybe it's about a different center.

Actually, let me reconsider the positions:
- A: x=2 to x=4, y=3 to y=6 (upper right)
- B: x=-4 to x=-2, y=-1 to y=-3 (lower left, but closer to origin than A)

For 90° CCW about origin: A at (2-4, 3-6) → (-6 to -3, 2 to 4). That's upper left, not lower left.

For 90° CW about origin: A at (2-4, 3-6) → (3 to 6, -4 to -2). That's lower right.

For 180° about origin: A at (2-4, 3-6) → (-4 to -2, -6 to -3). That's lower left! And the house would be upside down (peak pointing down).

If B is actually a house pointing down (not left), then 180° rotation about origin works!

Let me go with rotation 180° about the origin for problem 9.

Wait, but the description says B looks like it's pointing left. Let me reconsider.

Actually, looking at the image more carefully for problem 9:
- A is a house shape (pentagon) in upper right, peak pointing up
- B is described as a teal shape in lower left

If B is also a house shape but rotated, and it's in lower left...

Rotation 180° about origin would put the house upside down in lower left. That seems right!

So problem 9: Rotation 180° about the origin.

Let me finalize my answers:

1) Reflection in the y-axis (line x=0)
2) Rotation 90° clockwise about the origin
3) Reflection in the x-axis (line y=0)
4) Reflection in the y-axis (line x=0)
5) Rotation 180° about the origin
6) Reflection in the line y=-1
7) Rotation 180° about the origin
8) Rotation 180° about the origin
9) Rotation 180° about the origin

Hmm, having so many 180° rotations seems suspicious. Let me reconsider some of these.

Problem 7: Let me look again. A is orange L-shape in lower right, B is teal L-shape in upper left. If they're the same orientation (just translated and rotated), it could be 180° rotation. But if B is a mirror image, it could be reflection.

Looking at L-shapes: if A is ┘ (bottom-right corner filled) and after 180° rotation becomes (top-left corner filled), that matches B being in upper left.

Yes, 180° rotation about origin for problem 7.

Problem 8: Similar analysis. A in lower right, B in upper left. 180° rotation.

Problem 9: House in upper right, after 180° rotation would be upside-down house in lower left. Yes.

OK so my answers seem consistent. Let me double-check problem 6 though.

Problem 6: A at lower area (y=-4 to -6), B at upper area (y=2 to 4), both at similar x positions (x=-4 to -2).

If reflection in horizontal line y=k:
A at y=-5 (center) → B at y=3 (center)
Midpoint: (-5+3)/2 = -1
So reflection in y=-1. ✓

Actually wait, let me reconsider. If A is at y=-4 to y=-6 and B is at y=2 to y=4:
- A's top edge at y=-4 reflects to y=2 (B's bottom edge)? Midpoint: (-4+2)/2 = -1 ✓
- A's bottom edge at y=-6 reflects to y=4 (B's top edge)? Midpoint: (-6+4)/2 = -1 ✓

Yes, reflection in line y=-1.

Final answers:
1) Reflection in the y-axis
2) Rotation 90° clockwise about the origin
3) Reflection in the x-axis
4) Reflection in the y-axis
5) Rotation 180° about the origin
6) Reflection in the line y = -1
7) Rotation 180° about the origin
8) Rotation 180° about the origin
9) Rotation 180° about the origin

Hmm, I'm getting too many 180° rotations. Let me reconsider problems 7, 8, and 9 more carefully.

Problem 7: Looking at the L-shapes again. If A is in lower right and B is in upper left, and they look like mirror images across y=-x line...

Reflection in y=-x: (x,y) → (-y,-x)
If A has vertex at (2,-2), after reflection: (2,-2) → (2,-2)... that's on the line.
If A has vertex at (3,-1), after reflection: (1,-3). That's still lower right.

Hmm, that doesn't move it to upper left.

What about reflection in y=x? (x,y) → (y,x)
(2,-2) → (-2,2). That's upper left! ✓

Let me check: if A is at x=1 to x=3, y=-1 to y=-3:
After reflection in y=x: x=-3 to x=-1, y=1 to y=3. That's upper left!

And the L-shape orientation: if A is shape, after reflection in y=x it becomes shape (rotated differently).

Hmm, but does B look like └ shape?

Actually, I think I need to look at this more carefully. Let me assume the answer is rotation 180° about origin for now, since that's the most common transformation for shapes in opposite quadrants.

Actually, you know what, let me reconsider all the L-shape problems (7 and 8) and the house problem (9).

For problem 7: If A and B are both L-shapes in opposite quadrants, and they appear to have the same "handedness" (both are ┘ or both are ┌ when viewed from their respective positions), then it's 180° rotation. If they have opposite handedness, it's reflection.

I'll stick with 180° rotation about origin for problem 7.

For problem 8: Same analysis. 180° rotation about origin.

For problem 9: House shape. If A is pointing up and B is pointing down (upside down), it's 180° rotation. If B is pointing left or right, it's 90° rotation.

Based on B being in lower left, I'll say 180° rotation about origin (house upside down).

OK finalizing:

1) Reflection in the y-axis (x = 0)
2) Rotation 90° clockwise about the origin (0, 0)
3) Reflection in the x-axis (y = 0)
4) Reflection in the y-axis (x = 0)
5) Rotation 180° about the origin (0, 0)
6) Reflection in the line y = -1
7) Rotation 180° about the origin (0, 0)
8) Rotation 180° about the origin (0, 0)
9) Rotation 180° about the origin (0, 0)

Actually, I realize I should double-check problem 8 more carefully since having three consecutive 180° rotations seems odd for a worksheet.

Problem 8: A (orange L) in lower right, B (teal L) in upper left.

Let me think about this differently. What if it's rotation 90° counterclockwise about the origin?

If A is an L-shape with vertices at approximately (1,-2), (3,-2), (3,-3), (2,-3), (2,-5), (1,-5):
After 90° CCW: (2,1), (2,3), (3,3), (3,2), (5,2), (5,1)

That puts B at x=2 to x=5, y=1 to y=3. That's upper right, not upper left.

What about 90° clockwise?
(1,-2) → (-2,-1)
(3,-2) → (-2,-3)
(3,-3) → (-3,-3)
(2,-3) → (-3,-2)
(2,-5) → (-5,-2)
(1,-5) → (-5,-1)

That puts B at x=-5 to x=-2, y=-3 to y=-1. That's lower left, not upper left.

What about 180°?
(1,-2) → (-1,2)
(3,-2) → (-3,2)
(3,-3) → (-3,3)
(2,-3) → (-2,3)
(2,-5) → (-2,5)
(1,-5) → (-1,5)

That puts B at x=-3 to x=-1, y=2 to y=5. That's upper left! ✓

So 180° rotation about origin for problem 8. OK that confirms it.

Now for problem 7, let me do similar analysis:
If A is at approximately (1,-1), (3,-1), (3,-2), (2,-2), (2,-3), (1,-3):
After 180°: (-1,1), (-3,1), (-3,2), (-2,2), (-2,3), (-1,3)

That puts B at x=-3 to x=-1, y=1 to y=3. Upper left! ✓

And for problem 9:
If A (house) has vertices at approximately (2,3), (4,3), (4,5), (3,6), (2,5):
After 180°: (-2,-3), (-4,-3), (-4,-5), (-3,-6), (-2,-5)

That puts B at x=-4 to x=-2, y=-6 to y=-3. Lower left, upside down house! ✓

Great, so my answers are consistent.

Let me finalize:

1) Reflection in the y-axis
2) Rotation 90° clockwise about the origin
3) Reflection in the x-axis
4) Reflection in the y-axis
5) Rotation 180° about the origin
6) Reflection in the line y = -1
7) Rotation 180° about the origin
8) Rotation 180° about the origin
9) Rotation 180° about the origin