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 coordinates of \(A\), \(B\), \(C\)

From the graph, \(A(-1,2)\), \(B(2,2)\), \(C(-1,1)\)

Step2: Apply dilation formula

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

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

Answer:

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