Question

Dialations: Scale Factor Screenshot

Answer 1

The length of the segment
`A^(1)`
`E^(1)` is 5 units.

Explanation:

Step 1; First we calculate the length of segment AE in the pentagon ABCDE. To do this we use the formula

Distance = √ (x2 - x1)² + (y2 - y1)².

By plotting the points A and E we get their coordinates as A = (11, 3) and E = (11, 5). So distance between A (11, 3) and E (11, 5) where A is (x1, y1) and E is (x2, y2) is;

Distance = √ (11 - 11)² + (5 - 3)² = √ 0 + 4 = √4 = 2 units.

Step 2; To calculate the length of the segment
`A^(1)`
`E^(1)`, we multiply the scale factor with the length of the original segment length. So

Length of
`A^(1)`
`E^(1)` = Length of AE ×
`(5)/(2)` = 2 ×
`(5)/(2)` = 5 units.