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) =
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

Answer:

Coordinates of Vertices of triangle ABC are A (-4,3) , B(4,4) and C(1,1).

As, DO is Dilation of Δ ABC by Scale factor of $\frac{1}{2}$.

Vertices of A' B'C' are

$A'=(\frac{-4}{2},\frac{3}{2})=(-2,\frac{3}{2}), B'=(\frac{4}{2},\frac{4}{2})=(2,2), C'=(\frac{1}{2},\frac{1}{2})$

So, Image Δ A'B'C' will be smaller than the Pre image Δ ABC.

The two triangles will be congruent.

AO is Dilated by a factor of half , so A'O' will be half of AO.

So, correct Statements are

1. AB is parallel to A'B'.

2.DO,1/2(x, y) =  

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

$OA=\sqrt{(-4)^2+3^2}=\sqrt{25}=5\\\\ O'A'=\sqrt{2^2+(\frac{3}{2})^2}=\frac{5}{2}=2.5$

Answer 2

The correct answers are the first three options

1. AB is parallel to A'B'.2. DO,1/2(x, y) = 3. The distance from A' to the origin is half the distance from A to the origin