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 original points

Assume \( B(5,9) \), \( C(8,9) \), \( D(3, - 6) \).

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 \( B(5,9) \): \( (\frac{1}{3}\times5,\frac{1}{3}\times9)=(\frac{5}{3},3) \).
• For \( C(8,9) \): \( (\frac{1}{3}\times8,\frac{1}{3}\times9)=(\frac{8}{3},3) \).
• For \( D(3, - 6) \): \( (\frac{1}{3}\times3,\frac{1}{3}\times(-6))=(1,-2) \).

Step3: Plot new points

Plot \( B'(\frac{5}{3},3) \), \( C'(\frac{8}{3},3) \), \( D'(1,-2) \) and connect them to form the dilated image of \( \triangle BCD \).

Answer:

Plot the points \( (\frac{5}{3},3) \), \( (\frac{8}{3},3) \), and \( (1, - 2) \) on the coordinate plane and connect them.