Question

1. drag and drop the numbers into each of the boxes to complete the sentence. a triangle abc is dilated to obtain triangle abc as shown on the coordinate grid. the scale factor of the dilation is ( ), and the coordinates of the center of the dilation are ( )

Explanation:

Step1: Identify corresponding side lengths

Count the grid - units of corresponding sides of the original and dilated triangles. Let's assume a side of triangle \(ABC\) and its corresponding side of triangle \(A'B'C'\). If a side of \(\triangle ABC\) has a length of \(2\) units and the corresponding side of \(\triangle A'B'C'\) has a length of \(4\) units.

Step2: Calculate scale factor

The scale factor \(k\) of a dilation is given by the ratio of the length of a side of the dilated figure to the length of the corresponding side of the original figure. So \(k=\frac{\text{length of side in dilated triangle}}{\text{length of side in original triangle}}=\frac{4}{2} = 2\).
To find the center of dilation, we note that the lines connecting corresponding vertices (\(A\) to \(A'\), \(B\) to \(B'\), \(C\) to \(C'\)) intersect at the point \((2, - 2)\).

Answer:

The scale factor of the dilation is \(2\), and the coordinates of the center of the dilation are \((2,-2)\)