Question

question 2 points 2 the image of (3, -5) after a dilation with respect to the origin is (15, -25). what is the scale factor of the dilation? 4 5 6 12

Explanation:

Step1: Recall dilation formula

For a dilation with respect to the origin, the image of a point \((x,y)\) is \((kx,ky)\), where \(k\) is the scale factor.

Step2: Find scale factor using x - coordinates

Given the original point \((3, - 5)\) and the image \((15,-25)\). Using the x - coordinates: \(3k=15\). Solving for \(k\), we divide both sides by 3: \(k = \frac{15}{3}=5\). We can verify with the y - coordinates: \(- 5k=-25\), so \(k=\frac{-25}{-5} = 5\).

Answer:

B. 5