TransformationsDilating about the origin
Name: Date:
Dilate each point about the origin. Write where it lands.
1by scale factor ½ ()
2scale factor 2 ()
3by scale factor ½ ()
4by scale factor ½ ()
5scale factor 2 ()
6scale factor 2 ()
Dilations worksheets
A dilation is the transformation that changes size: every point moves toward or away from a center, and its distance is multiplied by a scale factor. These free printable worksheets scale a point from the origin and ask where it lands.
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Dilations
The answer key prints on a separate page.
What's on this sheet
The mixed transformation sheets slide, flip, and turn — three moves that keep a figure the same size. Dilation is the fourth, and it belongs on a page of its own because it is the one that does not: scaling by 3 sends the point (2, 3) to (6, 9), each coordinate multiplied by the factor. Keeping it separate is what lets a child see that this move is multiplication where the others were addition or a swap of signs.
Why this sheet works
The center here is the origin, which is the case with the clean rule: multiply both coordinates by the scale factor and you are done. The grid shows where the point starts, so a child can see it moving out along the line from the origin rather than jumping to an answer read off the squares.
How this one works
One question from this sheet, worked through a step at a time.
(2, −2) by scale factor ½
(2, −2)
2 × ½=1
−2 × ½=−1
(2, −2)→(1, −1)
- Start where the point is: (2, −2). The move is by scale factor ½, and the question is only where those two numbers end up.
- A dilation from the center O does not turn or flip — it SCALES. Multiply each coordinate by ½: 2 × ½ = 1, and −2 × ½ = −1.
- So it lands on (1, −1) — the same direction from O, half as far out.