P(2,3) , Q (1,3) and R (4,5) are vertices if a triangle PQR find length of median QS
Answers
Answer:
In △PQR,
P=(2,1)
Q=(−2,3)
R=(4,5)
Mid-point of PQ=(
2
x
1
+x
2
,
2
y
1
+y
2
)=(
2
2−2
,
2
1+3
)=(0,2)
Equation of the median through the vertex R is the equation of the line passing through the points (0,2),(4,5)
Since, two points form of the line is y−y
1
=(
x
2
−x
1
y
2
−y
1
)(x−x
1
)
∴ Equation of the median is
y−2=(
4−0
5−2
)(x−0)
⟹4(y−2)=3x
⟹4y−8=3x
3x−4y+8=0 (Ans)
Step-by-step explanation:
In △PQR,
P=(2,1)
Q=(−2,3)
R=(4,5)
Mid-point of PQ=(
2
x
1
+x
2
,
2
y
1
+y
2
)=(
2
2−2
,
2
1+3
)=(0,2)
Equation of the median through the vertex R is the equation of the line passing through the points (0,2),(4,5)
Since, two points form of the line is y−y
1
=(
x
2
−x
1
y
2
−y
1
)(x−x
1
)
∴ Equation of the median is
y−2=(
4−0
5−2
)(x−0)
⟹4(y−2)=3x
⟹4y−8=3x
3x−4y+8=0 (Ans)