Question

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

Explanation:

Step1: Identify original vertices

Let \(K(-1,-2)\), \(L(1,-2)\), \(M(1,1)\), \(N(-1,1)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 4\), the formula for a point \((x,y)\) is \((kx,ky)\).
For point \(K\): \((-1\times4,-2\times4)=(-4,-8)\)
For point \(L\): \((1\times4,-2\times4)=(4,-8)\)
For point \(M\): \((1\times4,1\times4)=(4,4)\)
For point \(N\): \((-1\times4,1\times4)=(-4,4)\)

Step3: Graph new rectangle

Plot the points \((-4,-8)\), \((4,-8)\), \((4,4)\), \((-4,4)\) and connect them to form the dilated rectangle.

Answer:

Plot the points \((-4,-8)\), \((4,-8)\), \((4,4)\), \((-4,4)\) and connect them to get the dilated rectangle of \(KLMN\).