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 the original rectangle

The coordinates of rectangle \(KLMN\) are \(K(-1,-1)\), \(L(0,-1)\), \(M(0,1)\), \(N(-1,1)\)

Step2: Apply the dilation formula

The formula for dilation centered at the origin \((x,y)\to(kx,ky)\) where \(k = 4\)

• For point \(K(-1,-1)\): \((-1\times4,-1\times4)=(-4,-4)\)
• For point \(L(0,-1)\): \((0\times4,-1\times4)=(0,-4)\)
• For point \(M(0,1)\): \((0\times4,1\times4)=(0,4)\)
• For point \(N(-1,1)\): \((-1\times4,1\times4)=(-4,4)\)

Step3: Plot the new points

Plot the points \((-4,-4)\), \((0,-4)\), \((0,4)\), \((-4,4)\) on the coordinate plane and connect them to form the dilated rectangle.

Answer:

The coordinates of the dilated rectangle are \(K'(-4,-4)\), \(L'(0,-4)\), \(M'(0,4)\), \(N'(-4,4)\). Plot these points and connect them to get the image of rectangle \(KLMN\) after dilation.