Question

Parallelogram with vertices A(-2, -1), B (-3, 2), C (1, 3), and D (2, 0) is drawn on a coordinate grid.



Suppose the parallelogram is dilated in reference to the origin using a magnitude of 2.



What would be the coordinates of the new vertices A'B'C'D'?



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Answer 1

A dilation about the origin with scale factor 2 multiplies each coordinate by 2. So for any point (x,y) the image is (2x, 2y).

Apply this to each vertex:

- A(-2, -1) → A' = (2·(-2), 2·(-1)) = (-4, -2)
- B(-3, 2) → B' = (2·(-3), 2·2) = (-6, 4)
- C( 1, 3) → C' = (2·1, 2·3) = ( 2, 6)
- D( 2, 0) → D' = (2·2, 2·0) = ( 4, 0)

Therefore the dilated vertices are A'(-4, -2), B'(-6, 4), C'(2, 6), D'(4, 0).