Question

graph the image of \\( \triangle qrs \\) after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Find the coordinates of the original triangle

The coordinates of \(Q\) is \((-1,1)\), \(R\) is \((3,1)\) and \(S\) is \((-1,2)\)

Step2: Apply the dilation formula

For a dilation centered at the origin with scale factor \(k = 4\), the formula is \((x,y)\to(kx,ky)\)

• For \(Q(-1,1)\): \((-1\times4,1\times4)=(-4,4)\)
• For \(R(3,1)\): \((3\times4,1\times4)=(12,4)\)
• For \(S(-1,2)\): \((-1\times4,2\times4)=(-4,8)\)

Step3: Plot the new points

Plot the points \((-4,4)\), \((12,4)\) and \((-4,8)\) on the coordinate plane and connect them to form the dilated triangle.

Answer:

Plot the points \(Q'(-4,4)\), \(R'(12,4)\) and \(S'(-4,8)\) and connect them.