Question

1. graph the image of the triangle below using a scale factor of $k = 3/4$.

Explanation:

Step1: Determine the coordinates of \(A\), \(B\), and \(C\)

From the graph, \(A(- 2,8)\), \(B(6,4)\), \(C(0,0)\)

Step2: Apply the scale - factor formula \((x',y')=(k\times x,k\times y)\)

For point \(A\):
\(x'=\frac{3}{4}\times(-2)=-\frac{3}{2}\), \(y'=\frac{3}{4}\times8 = 6\), so \(A'(-\frac{3}{2},6)\)
For point \(B\):
\(x'=\frac{3}{4}\times6=\frac{9}{2}\), \(y'=\frac{3}{4}\times4 = 3\), so \(B'(\frac{9}{2},3)\)
For point \(C\):
\(x'=\frac{3}{4}\times0 = 0\), \(y'=\frac{3}{4}\times0=0\), so \(C'(0,0)\)

Answer:

\(A'(-\frac{3}{2},6)\), \(B'(\frac{9}{2},3)\), \(C'(0,0)\)