point p divides the line segment joinning the points A(2,1) and B(5,-8) such that AP/PB=1/3 if p lies on the - Maths - Coordinate Geometry

Question

point p divides the line segment joinning the points A(2,1) and
B(5,-8) such that AP/PB=1/3 if p lies on the line 2x - y +k=0 find
the value of k

Priyanka Kedia · Accepted Answer

Given, Point P divides the line segment in the ratio 1 : 3.

We know that, coordinates of the point dividing the line segment joining the points $(x_{1}, y_{1}) a n d (x_{2}, y_{2})$ in the ratio m : n is given by,

$(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$

Therefore,

$C o o r d i n a t e o f p o int P = (\frac{1 \times 5 + 3 \times 2}{1 + 3}, \frac{1 \times (- 8) + 3 \times 1}{1 + 3}) = (\frac{5 + 6}{4}, \frac{- 8 + 4}{4}) = (\frac{11}{4}, - 1) \Rightarrow C o o r d i n a t e o f p o int P = (\frac{11}{4}, - 1)$

Since point P lies on line 2x-y+k=0. So, point (11/4, -1) will satisfy this line. Therefore,

$2 (\frac{11}{4}) - (- 1) + k = 0 \Rightarrow \frac{11}{2} + 1 + k = 0 \Rightarrow \frac{13}{2} + k = 0 \Rightarrow k = - \frac{13}{2}$

Hence, value of k is -13/2.

point p divides the line segment joinning the points A(2,1) and B(5,-8) such that AP/PB=1/3.if p lies on the line 2x - y +k=0 find the value of k.