Q19Find the ratio in which x
axis divides the line segment
joining points A (-3 ,10) and B(6 ,– 8).Also find the point of
intersection.
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Q19Find the ratio in which x
axis divides the line segment
joining points A (-3 ,10) and B(6 ,– 8).Also find the point of
intersection.
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Answer:
Solution :-
Given x-axis divide the segment joining points
(2,−3) and (5,6)
Let the ratio be k:1
then x =
m
1
+m
2
m
1
x
2
+m
2
x
1
y=
m
1
+m
2
m
1
y
2
+m
2
y
1
=0
⇒
k+1
6k−3
=0
⇒6k=3
⇒k=
2
1
the ratio is 1:2
Step-by-step explanation:
Let the required ratio be λ;1. Then, the coordinates of the point of division are,
R( 6λ-3 , -8λ+10 )
( λ+1 λ+1 )
But, it is a point on x-axis on which y-coordinates of every point is zero.
∴ 6λ-3
λ+1
=0⇒λ= 1/2
Thus,the required ratio is 1/2 : 1 or, 1:2
Putting λ=1/2 in the coordinates of R, we find that its coordinates are (0,6)