Question

graph the image of \\( \triangle b c d \\) after a dilation with a scale factor of \\( \frac { 1 } { 3 } \\), centered at the origin.

Explanation:

Step1: Find coordinates of points

From the graph, \( B(6,9) \), \( C(9,9) \), \( D(3, - 6) \).

Step2: Apply dilation formula

The formula for dilation centered at the origin is \( (x,y)\to(\frac{1}{3}x,\frac{1}{3}y) \).
For \( B(6,9) \): \( (\frac{1}{3}\times6,\frac{1}{3}\times9)=(2,3) \).
For \( C(9,9) \): \( (\frac{1}{3}\times9,\frac{1}{3}\times9)=(3,3) \).
For \( D(3,-6) \): \( (\frac{1}{3}\times3,\frac{1}{3}\times(-6))=(1,-2) \).

Step3: Plot the new points

Plot \( B'(2,3) \), \( C'(3,3) \), \( D'(1,-2) \) and connect them to form the dilated \( \triangle B'C'D' \).

Answer:

The coordinates of the image of \( \triangle BCD \) after dilation are \( B'(2,3) \), \( C'(3,3) \), \( D'(1,-2) \). Plot these points on the coordinate - plane and connect them.