First slide

Equation of line in Straight lines

Question

If each of the point $(x_{1}, 4) (- 2, y_{1})$ lies on the line joining the points $(2, - 1)$ and $(5, - 3)$ , then the point $P (x_{1}, y_{1})$ lies on the line

Moderate

A

$6 (x + y) - 25 = 0$
B

$2 x + 6 y + 1 = 0$
C

$2 x + 3 y - 6 = 0$
D

$6 (x + y) + 25 = 0$

Solution

The equation of the line joining the points $(2, - 1)$ and $(5, - 3)$ is given by
$y + 1 = \frac{- 1 + 3}{2 - 5} (x - 2)$
or $2 x + 3 y - 1 = 0$
Since $(x_{1}, 4)$ and $(- 2, y_{1})$ lie on $2 x + 3 y - 1 = 0,$ we have
$2 x_{1} + 12 - 1 = 0$ or $x_{1} = - \frac{11}{2}$
and $- 4 + 3 y_{1} - 1 = 0$ or $y_{1} = \frac{5}{3}$
Thus, $(x_{1}, y_{1})$ satisfies $2 x + 6 y + 1 = 0$

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