# In What Ratio is the Line Segment Joining the Points A(-2, -3) and B(3,7) Divided by the Yaxis? Also, Find the Coordinates of the Point of Division. - Mathematics

In what ratio is the line segment joining the points A(-2, -3) and B(3,7) divided by the yaxis? Also, find the coordinates of the point of division.

#### Solution

Let AB be divided by the x-axis in the ratio :1 k at the point P.

Then, by section formula the coordination of P are

p = ((3k-2)/(k+1) , (7k-3)/(k+1))

But P lies on the y-axis; so, its abscissa is 0.
Therefore , (3k-2)/(k+1) = 0

⇒ 3k-2 = 0 ⇒3k=2 ⇒ k = 2/3 ⇒ k = 2/3

Therefore, the required ratio is 2/3:1which is same as 2 : 3
Thus, the x-axis divides the line AB in the ratio 2 : 3 at the point P.

Applying k= 2/3,  we get the coordinates of point.

p (0,(7k-3)/(k+1))

= p(0, (7xx2/3-3)/(2/3+1))

= p(0, ((14-9)/3)/((2+3)/3))

= p (0,5/5)

= p(0,1)

Hence, the point of intersection of AB and the x-axis is P (0,1).

Concept: Coordinate Geometry
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 18