Midsegment Practice

Question

Consider the triangle with the vertices: A=(1,2) B=(-1,8) C=(7,10)

a. find the midpoint M of Line Segment AB

b. find the midpoint N of Line Segment AC

c. Verify that Line Segment MN is parallel to Line Segment BC

Answer 1

M is (0,5) N is (4,6)

MN has slope 1/4, BC has slope 2/8= 1/4

Just take the averages of the x coordinates and of the y coordinates to get the midpoints

For M average -1 and 1 to get 0, and 8 and 2 to get 5

slope is the difference in y coordinates divided by the difference in x coordinates ("rise over run")

for MN slope is (6-5)/((4-0) = 1/4

for BC slope is (10-8)/(7--1) = 2/8 = 1/4

if slopes are equal, the lines are parallel