Chapter 12, Problem 15CP

To determine

To find: The coordinates of the vertices of the image after dilation by a scale factor of $0.25$ .

Answer to Problem 15CP

The vertices of the image after dilation by a scale factor of $0.25$ is $\text{<msup><mo>A</mo><mo>′</mo></msup> (-1,2), B(0,0}\text{.5), C(1,0)}$ of the coordinates. Hence the letter of the correct answer is ‘H’

Explanation of Solution

Given information: $△\text{ABC has vertices A(-4,8), B(0,2), and C(4,0) to find the coordinates}$

  $\text{of the vertices of the image after dilation by a scale factor of 0}\text{.25}$.

Calculation: Use the coordinate rule for a dilation with. $\text{k=0}\text{.25}$ to find the coordinates of the vertices of the image .

Then from the graph and $\Delta \text{ABC}$

  $\text{ (x,y)}\to \text{(0}\text{.25x,0}\text{.25y)}$

  $\text{A(-4,8)}\to \text{<msup><mo>A</mo><mo>′</mo></msup> (-1,2)}$

  $\text{B(0,2)}\to \text{<msup><mo>B</mo><mo>′</mo></msup> (0,}\text{.5)}$

  $\text{C(4,0)}\to \text{<msup><mo>C</mo><mo>′</mo></msup> (1,0)}$

Notice the relationships between the lengths and slopes of the sides of the triangles. Each side of $\Delta {\text{A}}_1{\text{B}}_1{\text{C}}_1$ is longer than its corresponding side by the scale factor. The corresponding sides are parallel because their slopes are the same.

Hence, The vertices of the image after dilation by a scale factor of $0.25$ is $\text{<msup><mo>A</mo><mo>′</mo></msup> (-1,2),B(0,0}\text{.5),C(1,0)}$ of the coordinates. Hence the letter of the correct answer is ‘H’