Mario is writing a coordinate proof to show that the perpendicular bisector of an isosceles triangle's base divides it into two triangles of equal area.

a triangle is graphed on a coordinate plane. the vertices of triangle are labeled as a, b and c. the vertex labeled as a lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as b lies on begin ordered pair x comma y end ordered pair. the vertex labeled as c lies on begin ordered pair 2 x comma 0 end ordered pair. point d lies on side a c. an altitude is drawn from point b to point d.

enter your answers in the boxes to complete mario's proof.

since a perpendicular bisector bisects a segment, the coordinates of d are (
,
).

in △bcd, the length of the base is
and the height is y. so an expression for the area of △bcd is 12xy .

in △abd, the length of the base is
and the height is
. so an expression for the area of △abd is 12xy .

comparing the two areas shows that the perpendicular bisector of an isosceles triangle divides the triangle into two triangles of equal area.