Question

12 what is the scale factor? scale factor = 1/2

Explanation:

Step1: Find length of corresponding sides

Let's assume a side of the original triangle \( \triangle ABC\). For example, if we consider the vertical distance from \(C\) to the \(x -\)axis (original triangle). If \(C=(0, - 6)\), and for the smaller triangle \(C'=(0,-3)\).

Step2: Calculate the scale factor

The scale factor \(k\) is given by the ratio of the length of a side of the image (smaller triangle) to the length of the corresponding side of the original triangle. Using the \(y -\)coordinates of \(C\) and \(C'\), the length of the side from \(C\) to the \(x -\)axis is \(6\) units and from \(C'\) to the \(x -\)axis is \(3\) units. The scale factor \(k=\frac{\text{length of side in image}}{\text{length of corresponding side in original}}=\frac{3}{6}\)

Answer:

\(\frac{1}{2}\)