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

Explanation:

Step1: Identify coordinates of trapezoid

Assume (K(-8,-8)), (L(-8,9)), (M(4,4)), (N(4,-8))

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor (k = \frac{1}{4}), the new coordinates ((x',y')) of a point ((x,y)) are given by (x'=\frac{1}{4}x) and (y'=\frac{1}{4}y). For point (K): (x_K'=\frac{1}{4}\times(-8)= - 2), (y_K'=\frac{1}{4}\times(-8)=-2) For point (L): (x_L'=\frac{1}{4}\times(-8)= - 2), (y_L'=\frac{1}{4}\times9=\frac{9}{4}=2.25) For point (M): (x_M'=\frac{1}{4}\times4 = 1), (y_M'=\frac{1}{4}\times4 = 1) For point (N): (x_N'=\frac{1}{4}\times4 = 1), (y_N'=\frac{1}{4}\times(-8)=-2)

Step3: Plot new points

Plot the points (K'(-2,-2)), (L'(-2,2.25)), (M'(1,1)), (N'(1,-2)) and connect them to form the dilated trapezoid.

Answer:

Plot the points (K'(-2,-2)), (L'(-2,2.25)), (M'(1,1)), (N'(1,-2)) and connect them.