Question

A has the coordinates (–4, 3) and B has the coordinates (4, 4). If DO,1/2(x, y) is a dilation of △ABC, what is true about the image △A'B'C'? Check all that apply.

AB is parallel to A'B'.

DO,1/2(x, y) = (1/2x, 1/2y)

The distance from A' to the origin is half the distance from A to the origin.

The vertices of the image are farther from the origin than those of the pre-image.

A'B' is greater than AB.

Answer 1

A dilation is a transformation $D_{o,k}(x,y)$, with center O and a scale factor of k that is not zero, that maps O to itself and any other point P to P'. The center O is a fixed point, P' is the image of P, points O, P and P' are on the same line.

In a dilation of $D_{o, \frac{1}{2} }(x,y)$, the scale factor, $\frac{1}{2}$ is mapping the original figure to the image in such a way that the distances from O to the vertices of the image are half the distances from O to the original figure. Also the size of the image is half the size of the original figure.

Therefore, If $D_{o, \frac{1}{2} }(x,y)$ is a dilation of △ABC, the truth about the image △A'B'C' are:

AB is parallel to A'B'.

$D_{o, \frac{1}{2} }(x,y)=( \frac{1}{2}x, \frac{1}{2}y)$

The distance from A' to the origin is half the distance from A to the origin.

Answer 2

A: AB is parallel to A'B'.

B: DO,1/2(x, y) = (one-half x, one-half y)

C: The distance from A' to the origin is half the distance from A to the origin.