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Q.
If each of the points $(x_1 , 4), (-2 , y_1)$ lies on the line joining the points $(2, -1)$ and $(5, -3)$, then the point $P (x_1, y_1)$ lies on the line
Straight Lines
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 $2x + 3y - 1 = 0\,...(i)$
Since $(x_1, 4)$ and $(-2, y_1)$ lie on $2x + 3y -1 = 0$, we have
$2x_1 + 12 - 1 = 0$ or $x_1 = - \frac{11}{2}$
and $-4 + 3y_1 - 1 = 0$ or $y_1 = \frac{5}{3}$
Thus, $(x_1, y_1)$ satisfies $2x + 6y + 1 = 0$.