# The Line Joining the Points (2, 1) and (5, -8) is Trisected at the Points P And Q. If Point P lies on the Line 2x - Y + K = 0. Find the Value of K. - Mathematics

The line joining the points (2, 1) and (5, -8) is trisected at the points P and Q. If point P lies on the line 2x - y + k = 0. Find the value of k.

#### Solution

We have two points A (2, 1) and B (5,-8). There are two points P and Q which trisect the line segment joining A and B.

Now according to the section formula if any point P divides a line segment joining A(x_1,y_1) and B(x_2,y_2)in the ratio m: n internally than,

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

The point P is the point of trisection of the line segment AB. So, P divides AB in the ratio 1: 2

Now we will use section formula to find the co-ordinates of unknown point A as,

p(x_1,y_1) = ((1(5) + 2(2))/(1 + 2)"," (2(1) + 1(-8))/(1 + 2))

Therefore, co-ordinates of point P is(3,-2)

It is given that point P lies on the line whose equation is 2x - y + k = 0

So point A will satisfy this equation.

2(4) - 0 + k = 0

So,

k = -8

Concept: Coordinate Geometry
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#### APPEARS IN

RD Sharma Class 10 Maths
Chapter 6 Co-Ordinate Geometry
Exercise 6.3 | Q 53 | Page 31