Question

graph the image of trapezoid cdef after a dilation with a scale factor of $\frac{1}{4}$, centered at the origin.

Explanation:

Step1: Identify the vertices of trapezoid CDEF

The vertices are C(-8, - 4), D(8, - 4), E(4, 8), F(-8, 8).

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor $k=\frac{1}{4}$, the formula to find the new coordinates $(x',y')$ of a point $(x,y)$ is $x' = kx$ and $y'=ky$.
For point C(-8, - 4):
$x_C'=\frac{1}{4}\times(-8)=-2$
$y_C'=\frac{1}{4}\times(-4)=-1$
For point D(8, - 4):
$x_D'=\frac{1}{4}\times8 = 2$
$y_D'=\frac{1}{4}\times(-4)=-1$
For point E(4, 8):
$x_E'=\frac{1}{4}\times4 = 1$
$y_E'=\frac{1}{4}\times8 = 2$
For point F(-8, 8):
$x_F'=\frac{1}{4}\times(-8)=-2$
$y_F'=\frac{1}{4}\times8 = 2$

Step3: Graph the new trapezoid

Plot the points C'(-2,-1), D'(2,-1), E'(1,2), F'(-2,2) and connect them to form the dilated trapezoid.

Answer:

The new vertices of the dilated trapezoid are C'(-2,-1), D'(2,-1), E'(1,2), F'(-2,2). Graph these points to get the dilated trapezoid.