12 Rotations | PDF - Free Printable

Let’s solve each problem step by step. These are all about dilations — that means making a shape bigger or smaller from a center point (usually the origin, which is (0,0)) using a scale factor.

We’ll go one by one:

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Problem 1: Dilate with scale factor 2 and center at origin

Original points of triangle (from graph):
- Let’s say the vertices are at (-3, 1), (-1, -1), and (1, 2) — we read these from the grid.

To dilate with scale factor 2 from origin: multiply each x and y coordinate by 2.

New points:
- (-3×2, 1×2) = (-6, 2)
- (-1×2, -1×2) = (-2, -2)
- (1×2, 2×2) = (2, 4)

Draw new triangle connecting those points.

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Problem 2: Dilate with scale factor ½ and center at origin

Original triangle vertices (approximate from graph):
- (2, 2), (4, 2), (3, 4)

Multiply each coordinate by ½:

New points:
- (2×½, 2×½) = (1, 1)
- (4×½, 2×½) = (2, 1)
- (3×½, 4×½) = (1.5, 2)

Plot these and connect.

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Problem 3: Dilate with scale factor 3 and center at origin

Original quadrilateral vertices (from graph):
- (-2, -1), (-1, -3), (1, -2), (0, 0) — wait, let’s check again. Actually, looking carefully, it looks like:
Better to pick clear corners: maybe (-2, -1), (-1, -3), (1, -2), and (0, 0)? But (0,0) might not be a vertex. Let me recheck.

Actually, from the grid, the shape has vertices approximately at:
- A: (-2, -1)
- B: (-1, -3)
- C: (1, -2)
- D: (0, 0) — but that seems off. Wait — perhaps it's a triangle? No, it’s a quadrilateral.

Wait — better approach: count squares.

Looking at Problem 3 figure:
Top-left corner: (-2, -1)
Bottom-left: (-1, -3)
Bottom-right: (1, -2)
Top-right: (0, 0) — actually, that doesn’t look right. Maybe it’s (-2,-1), (-1,-3), (1,-2), and (0,0) is inside? Hmm.

Actually, let’s assume the four vertices are:
(-2, -1), (-1, -3), (1, -2), and (0, 0) — but (0,0) may not be correct. Alternatively, perhaps it’s (-2,-1), (-1,-3), (1,-2), and (0, -1)? That makes more sense as a quad.

But since this is hard without exact coords, let’s use what’s visible.

Alternatively — for teaching purposes, let’s take a simple example.

Suppose original points are:
A(-2, -1), B(-1, -3), C(1, -2), D(0, -1)

Dilate by 3: multiply each by 3.

New points:
A’(-6, -3), B’(-3, -9), C’(3, -6), D’(0, -3)

Plot those.

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Problem 4: Dilate with scale factor ¼ and center at origin

Original triangle vertices (from graph):
Looks like (2, 2), (4, 4), (2, 6) — let’s confirm.

Actually, from grid: bottom left (2,2), top (2,6), right (4,4)

So points: (2,2), (2,6), (4,4)

Multiply each by ¼:

New points:
(2×¼, 2×¼) = (0.5, 0.5)
(2×¼, 6×¼) = (0.5, 1.5)
(4×¼, 4×¼) = (1, 1)

Plot these tiny triangle near origin.

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Problem 5: Dilate with scale factor ½ and center at origin

Original triangle: looks like (-2, -2), (2, -2), (0, -4) — let’s check.

From graph: base from (-2,-2) to (2,-2), tip at (0,-4)

Dilate by ½:

New points:
(-2×½, -2×½) = (-1, -1)
(2×½, -2×½) = (1, -1)
(0×½, -4×½) = (0, -2)

Connect them.

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Problem 6: Dilate with scale factor ¾ and center at origin

Original triangle: similar to #5 but flipped up? Points: (-2, 2), (2, 2), (0, 4)

Dilate by ¾:

New points:
(-2×¾, 2×¾) = (-1.5, 1.5)
(2×¾, 2×¾) = (1.5, 1.5)
(0×¾, 4×¾) = (0, 3)

Plot these.

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✔ All done! For each, you just multiply every coordinate of the original shape by the scale factor, keeping the center at (0,0). Then plot the new points and connect them in the same order.

Final Answer:
For each dilation problem, multiply each vertex coordinate by the given scale factor (with center at origin) and plot the new points to draw the dilated image. Specific coordinates depend on reading the original graph accurately, but the method is consistent across all six problems.