Question

FIND THE RATIO IN WHICH THE Y-axis divides the line segment joining the points(6,-4) & (-2,-7).
ALSO FIND THE POINT OF INTERSECTION

Answer 1

The ratio in which the y-axis divides the line segment joining the points(6,-4) & (-2,-7) is 3:1.

( 0, -25/4 ) is the point of intersection.

Given,

Let P(6, -4) and Q(-2, -7)

Let the x-axis divides PQ in the ratio of β : 1.

Then the coordinates of the point of division are,

R (-2β+6/β+1 , -7β-4/β+1)

Since, R lies on y-axis and x-coordinate of every point on y-axis is zero.

∴ -2β+6/β+1 = 0

-2β + 6 = 0

-2β = -6

β = 3

Hence, the required ratio is 3:1

Putting β = 3 in the coordinates of R, we get the coordinates are

= (-2(3)+6/3+1 , -7(3)-4/3+1)

= ( -6+6/4 , -25/4 )

= ( 0, -25/4 )

Answer 2

Step-by-step explanation:

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