Find the ratio in which the Y-axis divides the line segment joining the points (5, -6)
and (-1, -4). Also find the point of intersection
Answers
Question :
Find the ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4). Also find the point of intersection.
Given :
Two points (5,-6) and (-1,-4)
To Find :
The ratio in which the y-axis divides the line segment joining the points (5,-6) and (-1,-4).
Solution :
Using Formula :
Now ,
By Cross Multiply :
Ratio is 5:1 .
Putting k = 5 in (y = -4k-6 / k+1) :
So , The Point of Intersection is 0 , -13/3 .
Let the line segment A(5, -6) and B(-1, -4) is divided at point P(0, y) by y-axis in ratio m:n
:. x = and y =
Here, (x, y) = (0, y); (x1, y1) = (5, -6) and (x2, y2) = (-1, -4)
So , 0 =
=> 0 = -m + 5n
=> m= 5n
=> =
=> m:n = 5:1
Hence, the ratio is 5:1 and the division is internal.Now,
y =
=> y =
=> y =
=> y =
=> y =
Hence, the coordinates of the point of division is (0, -13/3).
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