The length of the segment [tex]A^{1}[/tex][tex]E^{1}[/tex] is 5 units.
Step-by-step 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 [tex]A^{1}[/tex][tex]E^{1}[/tex], we multiply the scale factor with the length of the original segment length. So
Length of [tex]A^{1}[/tex][tex]E^{1}[/tex] = Length of AE × [tex]\frac{5}{2}[/tex] = 2 × [tex]\frac{5}{2}[/tex] = 5 units.
