A B C (O,5) (4,7) (1,3) respectively find an equation parallel to A B and passing through C ?
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11th
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Straight Lines
Various Forms of the Equation of a Line
In triangle ABC the co - or...
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Asked on December 30, 2019 by
Sanyog Khangwal
In triangle ABC the co-ordinates of vertices A, B and C are (4, 7), (-2, 3) and (0, 1) respectively. Find the equations of medians passing through vertices A, B and C.
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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
)
Using this formula,
mid point of AB =(
2
4−2
,
2
7+3
)=(1,5)
mid point of BC =(
2
−2+0
,
2
3+1
)=(−1,2)
mid point of CA =(
2
0+4
,
2
1+7
)=(2,4)
Equation
of a line joining two points (x
1
,y
1
) and (x
2
,y
2
) is given by the formula y−y
1
=(
x
2
−x
1
y
2
−y
1
)(x−x
1
)
Equation of Median passing through
A is the equation passing through A (4,7) and Midpoint of BC (−1.2) is y−7=(
−1−4
2−7
)(x−4)
=>y−7=
−5
−5
(x−4)
=>y−7=x−4
=>x−y+3=0