Question

The endpoints of sa020-1.jpg are A(9, 4) and B(5, – 4). The endpoints of its image after a dilation are sa020-2.jpg and sa020-3.jpg. Find the scale factor.

Answer 1

Answer:
The scale factor is (√10) / (4)

Explanation:
The complete question as well as the rule for the distance between two points are shown in the attached image.

To get the scale factor, we will follow these steps:
1- Length of AB:
AB = √(5-9)²+(-4-4)² 
AB = √80
AB = 4√5 units

2- Length of A'B':
A'B' = √(5-6)²+(-4-3)²
A'B' = √50
A'B' = 5√2

3- getting the scale factor:
A'B' = k AB where k is the scale factor
5√2 = k * 4√5
k = (√10) / (4)

Hope this helps :)