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# Find the Ratio in Which the Point (2, Y) Divides the Line Segment Joining the Points a (-2,2) and B (3, 7). Also, Find the Value of Y. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

Find the ratio in which the point (2, y) divides the line segment joining the points A (-2,2) and B (3, 7). Also, find the value of y.

#### Solution

The co-ordinates of a point which divided two points(x_1,y_1) and                  (x_2,y_2) internally in the ratio m:n is given by the formula,

(x,y) = ((mx_2 + nx_1)/(m + n)), ((my_2 + ny_1)/(m+n)))

Here we are given that the point P(2,y) divides the line joining the points A(−2,2) and B(3,7) in some ratio.

Let us substitute these values in the earlier mentioned formula.

(2,y) = (((m(3) +n(-2))/(m + n))"," ((m(7)+n(2))/(m+n)))

Equating the individual components we have

2 = (m(3) + n(-2))/(m + n)

2m + 2n = 3m - 2n

m - 4n

m/n = 4/1

We see that the ratio in which the given point divides the line segment is 4: 1.

Let us now use this ratio to find out the value of ‘y’.

(2,y) = (((m(3) + n(-2))/(m + n))"," ((m(7) + n(2))/(m + n)))

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

Equating the individual components we have

y = (4(7) + 1()2)/(4 + 1)

y = 6

Thus the value of ‘y’ is 6

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Solution Find the Ratio in Which the Point (2, Y) Divides the Line Segment Joining the Points a (-2,2) and B (3, 7). Also, Find the Value of Y. Concept: Concepts of Coordinate Geometry.
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