Question

Assertion :The equation of the straight line which passes through the point (2, -3) and the point of the intersection of the lines $x+y+4=0$ and $3x-y-8=0$ is $2x-y-7=0$ Reason: Product of slopes of two perpendicular straight lines is -1.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Given lines

$x+y+4=0$

$x=-y-4$-----(1)

$3x-y-8=0$-(2)

from eq (1) and (2)

$3(-y-4)-y-8=0$

$-3y-12-y-8=0$

$-4y=20$

$y=-5$

from eq(1)

$x=+5-4$

$x=1$

point of intersection $P(1,-5)$

eq of line from point A$(2,-3)$ and $P(1,-5)$

$y+3=\frac{-5+3}{1-2}(x-2)$

$y+3=\frac{-2}{-1}(x-2)$

$y+3=2x-4$

$2x-y-7=0$

if two line are perpendicular then

$m_1{m}_2=-1$

But the reason is not correct for statement