Question

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

Explanation:

Step1: Find coordinates of \( \triangle EFG \)

From the graph, \( E(-6,9) \), \( F(6,9) \), \( G(-6,-9) \)

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \( k=\frac{1}{3} \), the formula is \( (x,y)\to(kx,ky) \)
For point \( E(-6,9) \):
\( x'=\frac{1}{3}\times(-6)= - 2\), \( y'=\frac{1}{3}\times9 = 3\), so \( E'(-2,3) \)
For point \( F(6,9) \):
\( x'=\frac{1}{3}\times6 = 2\), \( y'=\frac{1}{3}\times9=3 \), so \( F'(2,3) \)
For point \( G(-6,-9) \):
\( x'=\frac{1}{3}\times(-6)=-2 \), \( y'=\frac{1}{3}\times(-9)= - 3\), so \( G'(-2,-3) \)

Step3: Plot the new points

Plot \( E'(-2,3) \), \( F'(2,3) \), \( G'(-2,-3) \) and connect them to form the dilated triangle.

Answer:

The coordinates of the image of \( \triangle EFG \) after dilation are \( E'(-2,3) \), \( F'(2,3) \), \( G'(-2,-3) \). Plot these points on the coordinate - plane and connect them.