Find the length of the segment with endpoint Y(4, 3) and midpoint M(1, 7).

Answer 1

Hi Brittina,

There are two ways to work this:

1. Find the distance between the endpoint Y and the midpoint M, then double it because from Y to M is half the distance across the segment OR
2. Find the other endpoint, and find the length of the segment using the two endpoints.

First way: dist from (4,3) to (1,7) = sqrt([4-1]²+[3-7]²) = sqrt(9+16) = sqrt(25) = 5

So from endpoint Y to the middle is 5 units. So distance to other endpoint is also 5 units, so the total lenght of the segment is 5 + 5 = 10.

Second way. From Y(4,3) to M(1,7) must move left 3 (start at x = 4 and end at x=1) and up 4 (start at y=3 and end at y=7). So now, repeat the same movements, but this time start at the midpoint.

Move left 3 units starting at x = 1 and end at x = -2

Move up 4 units starting at y=7 and end at y=11

So your other endpoint is at (-2,11). Now find the distance between (-2,11) and (4,3):

dist = sqrt([-2 - 4]² + [11 - 3]²) = sqrt([-6]² + [8]²) = squrt(36 + 64) = sqrt(100) = 10 units

Either way you solve it, the length of the segment is 10 units.