Ordered Pairs and Coordinate Plane Worksheets - Free Printable

Let’s solve each problem one by one. We’ll plot the points on a coordinate grid and then connect them in order to see what shape they form.

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Problem 1: Points (4,5), (6,2), (-2,-3), (-4,0)

Step 1: Plot each point.
- (4,5): Go right 4, up 5
- (6,2): Go right 6, up 2
- (-2,-3): Go left 2, down 3
- (-4,0): Go left 4, stay on x-axis

Step 2: Connect them in order: (4,5) → (6,2) → (-2,-3) → (-4,0) → back to (4,5)

Looking at the shape — it has four sides, no parallel sides obvious, but let’s check distances or just visualize.

Actually, if you draw this carefully, you’ll notice that opposite sides are equal and parallel? Let’s not guess — better to think of common shapes.

Wait — actually, plotting these:

From (4,5) to (6,2): goes right 2, down 3
From (6,2) to (-2,-3): goes left 8, down 5
That doesn’t look like a standard shape... Hmm.

Maybe I should calculate vectors or slopes? But for middle school level, we usually recognize by sight after plotting.

Alternatively — maybe it’s a quadrilateral with no special name? But the worksheet says “identify the shape”, so likely it’s a known shape.

Wait — let me try connecting differently? No, instruction says “in the given order”.

Perhaps I made a mistake. Let me list again:

Points: A(4,5), B(6,2), C(-2,-3), D(-4,0)

Plotting roughly:

A is top-rightish, B is further right but lower, C is bottom-left, D is left on x-axis.

Connecting A-B-C-D-A.

This looks like a kite? Or maybe a trapezoid?

Wait — let’s check midpoints or diagonals? Too advanced.

Actually, let’s do Problem 2 first — sometimes patterns help.

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Problem 2: Points (2,4), (5,4), (5,2), (2,2)

Plot:
- (2,4)
- (5,4) → same y, so horizontal line
- (5,2) → straight down from previous
- (2,2) → left to match x=2
- Back to (2,4) → up

This is clearly a rectangle! Actually, since all angles are 90° and opposite sides equal — yes, rectangle. Even better — width = 3 units (from x=2 to 5), height = 2 units (y=2 to 4). So definitely a rectangle.

But wait — is it a square? No, because 3 ≠ 2. So rectangle.

Actually — even more precise: it’s a rectangle, but since sides are aligned with axes, also called an axis-aligned rectangle.

But for school level, “rectangle” is fine.

Wait — actually, looking again: (2,4), (5,4), (5,2), (2,2) — yes, perfect rectangle.

So answer for #2: Rectangle

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Back to Problem 1: (4,5), (6,2), (-2,-3), (-4,0)

Let me try to sketch mentally:

Start at (4,5) — high up right
Go to (6,2) — further right, lower
Then to (-2,-3) — way left and down
Then to (-4,0) — a bit more left, up to x-axis
Back to (4,5) — long diagonal up-right

This seems irregular. Maybe it’s a quadrilateral with no special name? But the worksheet probably expects a specific name.

Wait — perhaps I miscalculated the order? Or maybe it’s a parallelogram?

Check vector AB: from (4,5) to (6,2) → Δx=+2, Δy=-3
Vector DC: from (-4,0) to (-2,-3)? Wait no — order is A→B→C→D→A

So vector BC: from (6,2) to (-2,-3) → Δx=-8, Δy=-5
Vector CD: from (-2,-3) to (-4,0) → Δx=-2, Δy=+3
Vector DA: from (-4,0) to (4,5) → Δx=+8, Δy=+5

Notice: AB = (2,-3), CD = (-2,3) → which is negative, so parallel and same length? Magnitude of AB: sqrt(4+9)=sqrt(13), CD: sqrt(4+9)=sqrt(13) — yes.

BC = (-8,-5), DA = (8,5) → also negatives, so parallel and same length.

So opposite sides are equal and parallel → this is a parallelogram!

Yes! So even though it’s tilted, it’s a parallelogram.

So Problem 1: Parallelogram

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Problem 3: Points (-3,1), (-1,3), (1,1), (-1,-1)

Plot:
- (-3,1)
- (-1,3) → right 2, up 2
- (1,1) → right 2, down 2
- (-1,-1) → left 2, down 2
- Back to (-3,1) → left 2, up 2

Connect in order.

This looks symmetric. Let’s see:

From (-3,1) to (-1,3): up-right
To (1,1): down-right
To (-1,-1): down-left
To (-3,1): up-left

Actually, this forms a diamond shape — all sides equal?

Calculate distances:

AB: from (-3,1) to (-1,3): dx=2, dy=2 → dist = √(4+4)=√8
BC: (-1,3) to (1,1): dx=2, dy=-2 → dist=√(4+4)=√8
CD: (1,1) to (-1,-1): dx=-2, dy=-2 → dist=√(4+4)=√8
DA: (-1,-1) to (-3,1): dx=-2, dy=2 → dist=√(4+4)=√8

All sides equal → rhombus.

Also, check diagonals: AC from (-3,1) to (1,1) → horizontal, length 4
BD from (-1,3) to (-1,-1) → vertical, length 4

Diagonals are perpendicular and equal? In a rhombus, diagonals are perpendicular bisectors. Here, one horizontal, one vertical → perpendicular. And both length 4 → so actually, it’s a square!

Because in a rhombus, if diagonals are equal, it’s a square.

Confirm angles: since diagonals are equal and perpendicular, and bisect each other — yes, it’s a square rotated 45 degrees.

So Problem 3: Square

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Problem 4: Points (0,0), (2,2), (4,2), (6,0), (4,-2), (2,-2)

Six points — so hexagon?

Plot:
- (0,0)
- (2,2) → up-right
- (4,2) → right
- (6,0) → down-right
- (4,-2) → down-left
- (2,-2) → left
- Back to (0,0) → up-left

This looks symmetric. Let’s see the shape.

It’s like a stretched hexagon. Notice symmetry over x-axis.

Points: top: (2,2),(4,2); bottom: (2,-2),(4,-2); ends: (0,0),(6,0)

Actually, this is a hexagon, but is it regular? No, because sides are not all equal.

Distance (0,0) to (2,2): √(4+4)=√8
(2,2) to (4,2): 2 units
(4,2) to (6,0): √(4+4)=√8
(6,0) to (4,-2): √(4+4)=√8
(4,-2) to (2,-2): 2 units
(2,-2) to (0,0): √(4+4)=√8

So sides alternate: √8, 2, √8, √8, 2, √8 — not all equal, so not regular.

But it has six sides → hexagon

Is there a more specific name? Like convex hexagon? But for school level, "hexagon" is sufficient.

Actually, looking at the shape — it resembles a boat or arrowhead, but technically, it's a hexagon.

Some might call it a "concave" hexagon? Let’s check internal angles.

At (2,2): coming from (0,0) to (2,2) to (4,2) — that’s a turn downward, angle less than 180? Actually, vector in: (2,2), out: (2,0) — dot product positive, so acute angle? Better not complicate.

Since all vertices are such that the polygon doesn't intersect itself and is simple, and has 6 sides — hexagon is correct.

But wait — actually, plotting it, it looks like two triangles attached? No.

Another thought: it’s symmetric and looks like a capital "H" but closed? Not really.

I think "hexagon" is acceptable.

But let me confirm with standard shapes. Perhaps it’s a regular hexagon? No, as sides differ.

So Problem 4: Hexagon

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Problem 5: Points (1,4), (4,4), (4,1), (1,1)

Similar to Problem 2.

Plot:
- (1,4)
- (4,4) → right 3
- (4,1) → down 3
- (1,1) → left 3
- Back to (1,4) → up 3

All sides equal? Distance between (1,4) and (4,4) is 3, (4,4) to (4,1) is 3, etc. All sides 3 units. Angles 90 degrees. So this is a square!

Yes — side length 3, aligned with axes.

So Problem 5: Square

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Problem 6: Points (-3,1), (-1,3), (1,1), (-1,-1)

Wait — this is identical to Problem 3!

Problem 3 was: (-3,1), (-1,3), (1,1), (-1,-1) — same points.

In the image, Problem 6 is written as: "(-3,1), (-1,3), (1,1), (-1,-1)" — yes, same as #3.

But in the user's image description, it might be different? Let me double-check the original input.

User wrote:

"5) (1,4), (4,4), (4,1), (1,1)"

"6) (-3,1), (-1,3), (1,1), (-1,-1)"

Yes, same as #3.

But in the actual image provided (though I can't see it, based on text), perhaps it's a typo? Or intentional?

Assuming it's correct, then Problem 6 is same as Problem 3: Square

But that seems odd for a worksheet to repeat. Maybe I misread.

Looking back at user's message:

"5) (1,4), (4,4), (4,1), (1,1)"

"6) (-3,1), (-1,3), (1,1), (-1,-1)"

Yes, identical to #3.

Perhaps in the original image, #6 is different? But based on text given, it's the same.

To be safe, I'll assume it's correct.

So Problem 6: Square

But let me confirm the points for #6: (-3,1), (-1,3), (1,1), (-1,-1) — same as #3.

Yes.

So answers:

1. Parallelogram
2. Rectangle
3. Square
4. Hexagon
5. Square
6. Square

But for #4, is there a better name? Some might say "irregular hexagon", but "hexagon" is fine.

Actually, upon second thought, Problem 4: points (0,0), (2,2), (4,2), (6,0), (4,-2), (2,-2)

If you connect them, it forms a shape that is symmetric and looks like a bowtie but closed — actually, it's a convex hexagon? Let me see the turns.

From (0,0) to (2,2) to (4,2): at (2,2), the direction changes from northeast to east — so turning right, angle greater than 90? Actually, the interior angle.

Perhaps it's easier to accept it as a hexagon.

I recall that this shape is sometimes called a "hexagon" or specifically a "convex hexagon", but for elementary level, "hexagon" suffices.

Another idea: it might be considered a "dodecagon"? No, only 6 points.

No, 6 vertices → hexagon.

So I'll stick with that.

Now, to write final answers clearly.

Final Answer:
1. Parallelogram
2. Rectangle
3. Square
4. Hexagon
5. Square
6. Square