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# Find the Ratio in Which the Line Segment Joining (-2, -3) and (5, 6) is Divided By Y-axis. Also, Find the Coordinates of the Point of Division in Each Case. - CBSE Class 10 - Mathematics

ConceptConcepts of Coordinate Geometry

#### Question

Find the ratio in which the line segment joining (-2, -3) and (5, 6) is divided by y-axis. Also, find the coordinates of the point of division in each case.

#### Solution

The ratio in which the x−axis divides two points (x_1,y_1) and (x_2,y_2) is λ : 1

The ratio in which the y-axis divides two points (x_1,y_1) and (x_2,y_2) is μ : 1

The coordinates of the point dividing two points (x_1,y_1)  and (x_2,y_2) in the ratio m:n is given as,

(x,y) = (((lambdax_2 + x_1)/(lambda + 1))","((lambday_2 + y_1)/(lambda + 1))) Where lambda = m/n

Here the two given points are A(−2,−3) and B(5,6).

The ratio in which the y-axis divides these points is (5mu - 2)/3 = 0

=> mu= 2/5

Let point P(x, y) divide the line joining ‘AB’ in the ratio 2: 5

Substituting these values in the earlier mentioned formula we have,

(x,y) = (((2/5(5) + (-2))/(2/5 + 1))","((2/5(6) + (-3))/(2/5 + 1)))

(x,y) = ((((10 + 5(-2))/5)/((2 + 5)/5)) "," (((12 + 5(-3))/3)/((2 + 5)/5)))

(x,y) = ((0/7)","(- 3/7))

(x,y) = (0, - 3/7)

Thus the ratio in which the x-axis divides the two given points and the co-ordinates of the point is 2:5 and (0, - 3/7)

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Solution Find the Ratio in Which the Line Segment Joining (-2, -3) and (5, 6) is Divided By Y-axis. Also, Find the Coordinates of the Point of Division in Each Case. Concept: Concepts of Coordinate Geometry.
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