Question

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

Explanation:

Step1: Find the coordinates of original points

From the graph, we can see that \(A(-2,2)\), \(B(2,2)\), \(C(-2,1)\)

Step2: Apply the dilation formula

The formula for dilation centered at the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 4\)

• For point \(A(-2,2)\): \((-2\times4,2\times4)=(-8,8)\)
• For point \(B(2,2)\): \((2\times4,2\times4)=(8,8)\)
• For point \(C(-2,1)\): \((-2\times4,1\times4)=(-8,4)\)

Step3: Plot the new points

Plot the points \(A'(-8,8)\), \(B'(8,8)\) and \(C'(-8,4)\) on the coordinate plane and connect them to form \(\triangle A'B'C'\)

Answer:

The coordinates of the image of \(\triangle ABC\) after dilation are \(A'(-8,8)\), \(B'(8,8)\) and \(C'(-8,4)\). Plot these points and connect them.