Question

1. scale factor: $\frac{1}{2}$

algebraic representation: ($\frac{1}{2}x,\frac{1}{2}y$)
a b (-1,4) c

Explanation:

Step1: Identify original coordinates

Assume \(A(-7,0)\), \(B(- 2,8)\), \(C(-2,-6)\) (by observing the graph).

Step2: Apply scale - factor formula

The algebraic representation for a scale - factor of \(\frac{1}{2}\) is \((\frac{1}{2}x,\frac{1}{2}y)\).
For point \(A\): \(x=-7,y = 0\), then \(A'=(\frac{1}{2}\times(-7),\frac{1}{2}\times0)=(-\frac{7}{2},0)\).
For point \(C\): \(x=-2,y=-6\), then \(C'=(\frac{1}{2}\times(-2),\frac{1}{2}\times(-6))=(-1,-3)\).

Answer:

\(A':(-\frac{7}{2},0)\), \(C':(-1,-3)\)