Lamar is writing a coordinate proof to show that a segment from the midpoint of the hypotenuse of a right triangle to the opposite vertex forms two triangles with equal areas. he starts by assigning coordinates as given.

a right triangle is graphed on a coordinate plane. the horizontal x-axis and y-axis are solid, and the grid is hidden. the vertices are labeled as m, k, and l. the vertex labeled as m lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as k lies on begin ordered pair 0 comma 2 b end ordered pair. the vertex labeled as l lies on begin ordered pair 2a comma 0 end ordered pair. a bisector is drawn from point m to the line kl. the intersection point on line kl is labeled as n.

enter the answers to complete the coordinate proof.
n is the midpoint of klkl¯ . therefore, the coordinates of n are (a,
).

to find the area of △knm△knm , the length of the base mk is 2b, and the length of the height is a. so an expression for the area of △knm△knm is
.

to find the area of △mnl△mnl , the length of the base ml is
, and the length of the height is
. so an expression for the area of △mnl△mnl is ab.

comparing the expressions for the areas shows that the areas of the triangles are equal.