Question

What are the coordinates of the endpoints of the midsegment for △LMN that is parallel to LN¯¯¯¯¯ ?

Enter your answers, as a decimal or whole number, in the boxes.
(
,
) and (
,
)

A triangle L M N is graphed on a coordinate plane. The horizontal x-axis ranges from 0 to 7 in increments of 1. The vertical y-axis ranges from 0 to 6 in increments of 1. The vertex labeled as l lies at begin ordered pair 0 comma 5 end ordered pair. The vertex labeled as M lies at begin ordered pair 6 comma 4 end ordered pair. The vertex labeled as N lies at begin ordered pair 0 comma 2 end ordered pair.

Answer 1

(3, 4.5) and (3, 3)

The midsegment of a triangle is a line connecting the midpoints of two sides of the triangle. So a triangle has 3 midsegments. Since you want the midsegment that's parallel to LN, we need to select the midpoints of LM and MN. The midpoint of a line segment is simply the average of the coordinates of each end point of the line segment. So:

Midpoint LM:

((0+6)/2, (5+4)/2) = (6/2, 9/2) = (3, 4.5)

Midpoint MN:

((6+0)/2, (4+2)/2) = (6/2, 6/2) = (3, 3)

So the desired end points are (3, 4.5) and (3, 3)