Question

raph the image of $\triangle uvw$ after a dilation with a scale factor of $\frac{1}{4}$, centered at the origin.

Explanation:

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

Assume \( U(8,-5) \), \( V(8,0) \), \( W(-10,-8) \).

Step2: Apply dilation formula

For a point \( (x,y) \) dilated with scale factor \( k=\frac{1}{4} \) centered at origin, new coordinates \( (x',y')=(kx,ky) \).
For \( U(8,-5) \):
\( x'=\frac{1}{4}\times8 = 2 \), \( y'=\frac{1}{4}\times(-5)=-\frac{5}{4} \), new point \( U'(2,-\frac{5}{4}) \).
For \( V(8,0) \):
\( x'=\frac{1}{4}\times8 = 2 \), \( y'=\frac{1}{4}\times0 = 0 \), new point \( V'(2,0) \).
For \( W(-10,-8) \):
\( x'=\frac{1}{4}\times(-10)=-\frac{5}{2} \), \( y'=\frac{1}{4}\times(-8)=-2 \), new point \( W'(-\frac{5}{2},-2) \).

Step3: Plot new points

Plot \( U'(2,-\frac{5}{4}) \), \( V'(2,0) \), \( W'(-\frac{5}{2},-2) \) and connect them to form \( \triangle U'V'W' \).

Answer:

Plot the points \( U'(2,-\frac{5}{4}) \), \( V'(2,0) \), \( W'(-\frac{5}{2},-2) \) and connect them.