Question

lesson 7: dilations in the coordinate plane
second slide - 2/4/26
a (1, 2) b (5, -6) c (2, -3) d (4, 10)
a (5, 10) b (25, -30) c (10, -15) d (20, 50)
what is the scale factor of this dilation?
k = ______

Explanation:

Step1: Recall dilation scale factor formula

The scale factor \( k \) of a dilation is found by dividing the coordinates of the image point by the coordinates of the original point. For a point \((x,y)\) dilated to \((x',y')\), \( k=\frac{x'}{x}=\frac{y'}{y} \).

Step2: Use point A and A' to calculate k

Take point \( A(1,2) \) and its image \( A'(5,10) \). Calculate \( k \) using the x - coordinates: \( k = \frac{5}{1}=5 \). Verify with y - coordinates: \( k=\frac{10}{2} = 5 \). We can also check with other points (e.g., \( B(5,-6) \) and \( B'(25,-30) \): \( \frac{25}{5}=5 \), \( \frac{-30}{-6}=5 \)) to confirm.

Answer:

\( 5 \)