In triangle ABC, the co-ordinate of A, B and C are (4,7) ,(-2,3) and (2,1) respectively . Find the length of the median.
Answers
Answer:
REFER IN ATTACHMENT
MARK AS BRAINLIST ANSWER PLEASE
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
Equation of Median passing through B is the equation passing through B
(−2,3) and Midpoint of AC (2,4) is y−3=(
2−(−2)
4−3
)(x−(−2))
=>y−3=
4
1
(x+2)
=>4y−12=x+2
=>x−4y+14=0
Equation of Median passing through C is the equation passing through C
(0,1) and Midpoint of AB (1,5) is y−1=(
1−0
5−1
)(x−0)
=>y−1=
1
4
(x)
=>y−1=4x
=>4x−y+1=0
