To find the distance between (-2,-3) and (4,1), peggy's teacher drew a diagram and marked blue lines to represent the legs of a right triangle. peggy then used 42 and 62 to find the distance represented by the red segment. what distance did she find ?

First, we find the distance between the two points. The equation is

d = √[(x1 - x2)² + (y1 - y2)²]
d = √[(-2 - 4)² + (-3 - 1)²]
d = 52

In a right triangle, the legs are the hypotenuse, the shorter and the longer side. The hypotenuse is the longest side, so this must be 62 units. So, she found the length of the longer side, which is 52 units.