Question

graph the image of rectangle klmn after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Find the coordinates of rectangle KLMN

Assume the coordinates of \(K(-1,-1)\), \(L(1,-1)\), \(M(1,1)\), \(N(-1,1)\) (from the graph where each grid is 1 unit).

Step2: Apply the dilation formula

The dilation formula centered at the origin is \((x,y)\to(kx,ky)\) where \(k = 4\).
For point \(K(-1,-1)\): \((-1\times4,-1\times4)=(-4,-4)\)
For point \(L(1,-1)\): \((1\times4,-1\times4)=(4,-4)\)
For point \(M(1,1)\): \((1\times4,1\times4)=(4,4)\)
For point \(N(-1,1)\): \((-1\times4,1\times4)=(-4,4)\)

Step3: Plot the new points

Plot the points \((-4,-4)\), \((4,-4)\), \((4,4)\), \((-4,4)\) on the coordinate plane and connect them to form the dilated rectangle.

Answer:

The new coordinates of the dilated rectangle are \(K'(-4,-4)\), \(L'(4,-4)\), \(M'(4,4)\), \(N'(-4,4)\). Graph these points and connect them to get the image of rectangle \(KLMN\) after dilation.