Question

graph the image of \\( \triangle abc \\) 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 the coordinates of \(A(-1,2)\), \(B(1,2)\), \(C(-1,1)\)

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

Step3: Plot the new points

Plot the points \(A'(-4,8)\), \(B'(4,8)\) and \(C'(-4,4)\) 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 \(A'(-4,8)\), \(B'(4,8)\) and \(C'(-4,4)\)