Enlargement - fractional and negative scale factors worksheet with nine exercises involving coordinate grids and geometric shapes.

Let’s solve each enlargement problem step by step. We’ll use the rule:

> To enlarge a shape with scale factor k and centre (a, b):
> - For each vertex of the shape, find the vector from the centre to that vertex.
> - Multiply that vector by the scale factor k.
> - Add the result back to the centre to get the new position.

We’ll do this for each part (a through i). Since we’re plotting on grid paper, we can count squares carefully.

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Part a: Scale factor -2, centre (0,2)

Original rectangle vertices (from grid):
Top-left: (-1, 3)
Top-right: (0, 3)
Bottom-right: (0, 1)
Bottom-left: (-1, 1)

Centre = (0, 2)

For each point:

1. (-1, 3):
Vector from centre: (-1 - 0, 3 - 2) = (-1, 1)
Multiply by -2: (2, -2)
New point: (0 + 2, 2 + (-2)) = (2, 0)

2. (0, 3):
Vector: (0, 1) → × -2 = (0, -2) → New: (0+0, 2-2) = (0, 0)

3. (0, 1):
Vector: (0, -1) → × -2 = (0, 2) → New: (0, 4)

4. (-1, 1):
Vector: (-1, -1) → × -2 = (2, 2) → New: (2, 4)

So new rectangle has corners at: (2,0), (0,0), (0,4), (2,4) — wait, let’s order them properly.

Actually, after transformation, the points are:
(2,0), (0,0), (0,4), (2,4) → This is a rectangle from x=0 to 2, y=0 to 4? Wait — no, let's list transformed points again:

From above:
(-1,3) → (2,0)
(0,3) → (0,0)
(0,1) → (0,4)
(-1,1) → (2,4)

So the new shape has vertices at: (0,0), (2,0), (2,4), (0,4) — yes, a rectangle 2 units wide, 4 units tall, sitting from x=0 to 2, y=0 to 4.

But note: since scale factor is negative, it’s also rotated 180° around the centre.

✔ Final shape for (a): Rectangle with corners at (0,0), (2,0), (2,4), (0,4)

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Part b: Scale factor -2, centre (1,2)

Original rectangle: looks like top-left (2,4), top-right (3,4), bottom-right (3,2), bottom-left (2,2)

Centre = (1,2)

Transform each:

1. (2,4): vector = (1,2) → × -2 = (-2,-4) → new = (1-2, 2-4) = (-1,-2)

2. (3,4): vector = (2,2) → × -2 = (-4,-4) → new = (1-4, 2-4) = (-3,-2)

3. (3,2): vector = (2,0) → × -2 = (-4,0) → new = (1-4, 2+0) = (-3,2)

4. (2,2): vector = (1,0) → × -2 = (-2,0) → new = (1-2, 2+0) = (-1,2)

So new rectangle: (-1,-2), (-3,-2), (-3,2), (-1,2)

That’s a rectangle from x=-3 to -1, y=-2 to 2.

✔ Final shape for (b): Rectangle with corners at (-3,-2), (-1,-2), (-1,2), (-3,2)

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Part c: Scale factor -2, centre (-1,-1)

Original rectangle: looks like bottom-left (-2,-3), bottom-right (1,-3), top-right (1,-2), top-left (-2,-2)

Wait — looking at grid: it spans from x=-2 to x=1 (width 3), y=-3 to y=-2 (height 1). So vertices:

(-2,-3), (1,-3), (1,-2), (-2,-2)

Centre = (-1,-1)

Transform each:

1. (-2,-3): vector = (-1,-2) → × -2 = (2,4) → new = (-1+2, -1+4) = (1,3)

2. (1,-3): vector = (2,-2) → × -2 = (-4,4) → new = (-1-4, -1+4) = (-5,3)

3. (1,-2): vector = (2,-1) → × -2 = (-4,2) → new = (-1-4, -1+2) = (-5,1)

4. (-2,-2): vector = (-1,-1) → × -2 = (2,2) → new = (-1+2, -1+2) = (1,1)

So new rectangle: (1,3), (-5,3), (-5,1), (1,1)

✔ Final shape for (c): Rectangle from x=-5 to 1, y=1 to 3

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Part d: Scale factor 0.5, centre (-5,0)

Original L-shape: Let’s identify key points.

From grid: It seems to be made of two rectangles.

Left vertical bar: from (-3,1) to (-3,4) and (-2,1) to (-2,4)? Wait — better to pick outer corners.

Actually, looking at the shape:

It goes from x=-3 to x=0, y=1 to y=4, but missing the bottom right square? No — actually, it’s an L-shape:

Points:
Top-left: (-3,4)
Top-right: (0,4)
Then down to (0,2), then left to (-2,2), then down to (-2,1), then left to (-3,1), then up to (-3,4)

So vertices in order: (-3,4), (0,4), (0,2), (-2,2), (-2,1), (-3,1)

Centre = (-5,0)

Apply scale factor 0.5 to each vector from centre.

Take one point: (-3,4)

Vector from (-5,0): (2,4) → ×0.5 = (1,2) → new = (-5+1, 0+2) = (-4,2)

Another: (0,4) → vector (5,4) → ×0.5 = (2.5,2) → new = (-5+2.5, 0+2) = (-2.5,2)

But we’re on grid — maybe we should use fractions or check if coordinates are integers.

Wait — perhaps the original shape has integer coordinates, and after scaling by 0.5 from (-5,0), we may get half-integers. But since it’s a grid, we plot exactly where they land.

Let’s compute all:

1. (-3,4): vec = (2,4) → ×0.5 = (1,2) → (-4,2)

2. (0,4): vec = (5,4) → ×0.5 = (2.5,2) → (-2.5,2)

3. (0,2): vec = (5,2) → ×0.5 = (2.5,1) → (-2.5,1)

4. (-2,2): vec = (3,2) → ×0.5 = (1.5,1) → (-3.5,1)

5. (-2,1): vec = (3,1) → ×0.5 = (1.5,0.5) → (-3.5,0.5)

6. (-3,1): vec = (2,1) → ×0.5 = (1,0.5) → (-4,0.5)

So the new shape will have these points. Since it’s a reduction by half toward the centre, it should look like a smaller L-shape closer to (-5,0).

✔ Final shape for (d): Plot points: (-4,2), (-2.5,2), (-2.5,1), (-3.5,1), (-3.5,0.5), (-4,0.5) — connect in order.

Note: In practice, students would draw this on grid, marking half-squares if needed.

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Part e: Scale factor 0.5, centre (1,-5)

Original house shape: pentagon.

Vertices approx:
Bottom-left: (0,-3)
Bottom-right: (2,-3)
Right side: (2,-1)
Roof peak: (1,0)
Left side: (0,-1)

Centre = (1,-5)

Transform each:

1. (0,-3): vec = (-1,2) → ×0.5 = (-0.5,1) → new = (1-0.5, -5+1) = (0.5,-4)

2. (2,-3): vec = (1,2) → ×0.5 = (0.5,1) → new = (1+0.5, -5+1) = (1.5,-4)

3. (2,-1): vec = (1,4) → ×0.5 = (0.5,2) → new = (1.5,-3)

4. (1,0): vec = (0,5) → ×0.5 = (0,2.5) → new = (1,-2.5)

5. (0,-1): vec = (-1,4) → ×0.5 = (-0.5,2) → new = (0.5,-3)

So new shape: (0.5,-4), (1.5,-4), (1.5,-3), (1,-2.5), (0.5,-3)

✔ Final shape for (e): Smaller house centered near (1,-5), half size.

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Part f: Scale factor -2, centre (-1,0)

Original triangle: right triangle with vertices at (-3,1), (-3,0), (-2,0)

Centre = (-1,0)

Transform:

1. (-3,1): vec = (-2,1) → × -2 = (4,-2) → new = (-1+4, 0-2) = (3,-2)

2. (-3,0): vec = (-2,0) → × -2 = (4,0) → new = (3,0)

3. (-2,0): vec = (-1,0) → × -2 = (2,0) → new = (1,0)

So new triangle: (3,-2), (3,0), (1,0)

✔ Final shape for (f): Triangle with those three points.

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Part g: Scale factor -0.5, centre (-1,-2)

Original trapezoid: vertices approx (-3,0), (-1,0), (0,-1), (-3,-1)

Wait — from grid: looks like quadrilateral with points:

(-3,0), (-1,0), (0,-1), (-3,-1)

Centre = (-1,-2)

Transform each:

1. (-3,0): vec = (-2,2) → × -0.5 = (1,-1) → new = (-1+1, -2-1) = (0,-3)

2. (-1,0): vec = (0,2) → × -0.5 = (0,-1) → new = (-1, -3)

3. (0,-1): vec = (1,1) → × -0.5 = (-0.5,-0.5) → new = (-1.5, -2.5)

4. (-3,-1): vec = (-2,1) → × -0.5 = (1,-0.5) → new = (0, -2.5)

So new shape: (0,-3), (-1,-3), (-1.5,-2.5), (0,-2.5)

✔ Final shape for (g): Quadrilateral with those points.

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Part h: Scale factor 0.5, centre (1,2)

Original rectangle: from (0,0) to (2,4)? Wait — looking at grid: it spans x=0 to 2, y=0 to 4? Actually, from image: it’s from x=0 to 2, y=0 to 4? Wait no — centre is (1,2), and shape is symmetric?

Actually, from grid: rectangle with corners (0,0), (2,0), (2,4), (0,4)

Centre = (1,2)

Transform each corner:

1. (0,0): vec = (-1,-2) → ×0.5 = (-0.5,-1) → new = (0.5,1)

2. (2,0): vec = (1,-2) → ×0.5 = (0.5,-1) → new = (1.5,1)

3. (2,4): vec = (1,2) → ×0.5 = (0.5,1) → new = (1.5,3)

4. (0,4): vec = (-1,2) → ×0.5 = (-0.5,1) → new = (0.5,3)

So new rectangle: (0.5,1), (1.5,1), (1.5,3), (0.5,3)

✔ Final shape for (h): Small rectangle centered at (1,2), half size.

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Part i: Scale factor -3, centre (-1,-1)

Original small triangle: vertices (-1,-2), (0,-2), (0,-3)

Centre = (-1,-1)

Transform:

1. (-1,-2): vec = (0,-1) → × -3 = (0,3) → new = (-1,2)

2. (0,-2): vec = (1,-1) → × -3 = (-3,3) → new = (-4,2)

3. (0,-3): vec = (1,-2) → × -3 = (-3,6) → new = (-4,5)

So new triangle: (-1,2), (-4,2), (-4,5)

✔ Final shape for (i): Large triangle pointing up-left.

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## Final Answer:

Since the task asks to “plot” the enlarged shapes, and we cannot draw here, the final answer is the set of transformed coordinates for each part. However, as per instruction, we provide only the final correct answer — which in this case is the completed plots. But since we must output text, we summarize the key results:

For each part, the enlarged shape is determined by applying the scale factor from the given centre. The exact coordinates of the new vertices are as calculated above.

If you are to plot them:

- Use the centre point.
- For each vertex, move from centre to vertex, multiply that distance/direction by scale factor, and mark the new point.
- Connect the new points to form the enlarged shape.

All calculations have been verified step by step.

✔ Final Answer: The enlarged shapes are plotted using the transformed coordinates as computed for parts (a) through (i) above. Each shape is correctly scaled and positioned relative to its centre of enlargement.