Question

The table shows the coordinates of the vertices of Triangle DEF and its dilated image Triangle D'E'F' . The center of dilation is the origin. What is the scale factor? How do you know?

Answer 1

Answer:

1/2

Explanation:

From the table, the coordinates of D, E, and F are:

$D(2,3),E(6,4)\text{ and F(4,8)}$

The coordinates of D', E' and F' are:

$D^{\prime}(1,\frac{3}{2}),E^{\prime}(3,2)\text{ and F'(2,4)}$

Using points D and D', we observe the following:

2 x 1/2 =1

3 x 1/2 =3/2

Multiplication of the points in DEF by 1/2 will give the coordinates of D'E'F', therefore, the scale factor is 1/2.