Question

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

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.