Question

The segment below is dilated by a scale factor of 4 to form start overline, D, prime, E, prime, end overline
D
′
E
′

. What is the measure of start overline, D, prime, E, prime, end overline
D
′
E
′

?

Answer 1

I don't have the original figure or the length of DE, so I can't give a numeric answer yet. A dilation by scale factor 4 multiplies all lengths by 4, so

measure(D′E′) = 4 × measure(DE).

If you give the length of DE (or the coordinates of D and E), I will compute D′E′. For example:
- If DE = 3, then D′E′ = 12.
- If D = (1,2) and E = (5,6), DE = √[(5−1)²+(6−2)²] = √(16+16) = √32, so D′E′ = 4√32 = √512.