What will be the length of the median through vertex A if the coordinates of the vertices of Δ ABC are A(2,5), B(5,0), C(-2,5) ?
a) √13/√2
b) √13/2
c) 13/√2
d) √13/4
Answers
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Step-by-step explanation:
A(5,1),B(1,5)andC(−3,−1) are the vertices of △ABCD
AD,BE and CF are medians.
We have mid point formula,
P(X,Y)=(
2
x
1
+x
2
,
2
y
1
+y
2
)
Coordinate of point D(
2
1−3
,
2
5−1
)=(−1,2)
∴AD=
(−1−5)
2
,(2−1)
2
=
36+1
=
37
Units
Coordinate of point E(
2
5−3
,
2
1−1
)=(1,0)
BE=
(1−1)
2
(0−5)
2
=
25
=5 units
Coordinate of point F(
2
5+1
,
2
1+5
)=(3,3)
∴
(−3−3)
2
+(−1−3)
2
=
36+16
=
52
=2
13
units
Attachments:
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