The medians ab and be of the triangle with the vertices A(0,b), B(0,0) and C(a,0) are mutually perpendicular if : A) b = root2a B) a = root2b C) b = -root2a D) a = -root2b
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A median in a triangle is a line passing thought a vertex and through the midpoint of the side opposite to the vertex.
D is the midpoint of side BC
D=(
2
a
,0)
slope of AD=
0−a/2
b−0
=
a
−2b
E is the midpoint of side AC
D=(
2
a
,
2
b
)
slope of BE=
0−a/2
0−b/2
=
a
b
If two lines are perpendicular, product of their slopes is -1.
(
a
−2b
)(
a
b
)=−1
2b
2
=a
2
a=±b
2
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