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the ratio in which y-axis divides the line joining the point P(-4,5) and Q(3,-7) is ?

the ratio in which y-axis divides the line joining the point P(-4,5) and Q(3,-7) is ?

Grade:Select Grade

1 Answers

Latika Leekha
askIITians Faculty 165 Points
6 years ago
Hello student,
Suppose it divides the line segment in the ratio k :1.
Then , we know that the coordinates of the point dividing the line segment joining (x1, y1) and (x2, y2) in the ratio m : n is given by
[(mx2+nx1)/(m+n), (my2+ny1)/(m+n))]
Here, (x1, y1) = (-4,5) and and (x2, y2) = (3,-7)
So, coordinates of point of intersection of PQ with y-axis (using the above formula)
=[(3k-4)/(k+1), (-7k+5)/(k+1)]
The x-coordinate of the point of the point of intersection of PQ and y-axis = 0
So, (3k-4)/(k+1) = 0
This gives k = 4/3
Hence, the required ratio is 4:3.

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