Question

graph the image of square abcd after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.

Explanation:

Step1: Identify the coordinates of the square vertices

Let \(A(- 10,-10)\), \(B(5,-10)\), \(C(5,5)\), \(D(-10,5)\)

Step2: Apply the dilation formula

For a dilation centered at the origin with scale - factor \(k = \frac{1}{5}\), the formula for the coordinates of a point \((x,y)\) after dilation is \((x',y')=(k x,k y)\)
For point \(A(-10,-10)\): \(x'=\frac{1}{5}\times(-10)= - 2\), \(y'=\frac{1}{5}\times(-10)=-2\)
For point \(B(5,-10)\): \(x'=\frac{1}{5}\times5 = 1\), \(y'=\frac{1}{5}\times(-10)=-2\)
For point \(C(5,5)\): \(x'=\frac{1}{5}\times5 = 1\), \(y'=\frac{1}{5}\times5 = 1\)
For point \(D(-10,5)\): \(x'=\frac{1}{5}\times(-10)=-2\), \(y'=\frac{1}{5}\times5 = 1\)

Step3: Plot the new points

Plot the points \(A'(-2,-2)\), \(B'(1,-2)\), \(C'(1,1)\), \(D'(-2,1)\) and connect them to form the dilated square.

Answer:

Plot the points \(A'(-2,-2)\), \(B'(1,-2)\), \(C'(1,1)\), \(D'(-2,1)\) and connect them to get the dilated square.