A(4,3),B(3,4),C(-3,-4) are vertices of a triangle. The length of median through A on BC is.......................units.
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Answer:
A median of a triangle is a line segment that joins the
vertex of a triangle to the midpoint of the opposite side.
Mid point of two points (x
1
,y
1
) and (x
2
,y
2
) is calculated by the formula (
2
x
1
+x
2
,
2
y
1
+y
2
)
Since AD is the median, this means, D is the mid point of BC.
Using this formula, mid point of BC =(
2
7−2
,
2
2−5
)=(
2
5
,
2
−3
)
Distance between two points (x
1
,y
1
) and (x
2
,y
2
) can be calculated using the formula
(x
2
−x
1
)
2
+(y
2
−y
1
)
2
Hence, length of AD =
(
2
5
−3)
2
+(
2
−3
−4)
2
=
4
1
+
4
121
=
4
122
=
2
122
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