Question

The equation of a line passing through (2, 3) and perpendicular to the line joining (-5, 6) and (-6, 5) is _______.

• A. x+y+5=0
• B. x-y+5=0
• C. x-y=5
• D. x+y=5

Answer 1

Answer: (D)

x+y=5

Given equation of line joining (-5,6) and (-6,5);

$m_1=\frac{y_2-y_1}{x_2-x_1}$

$m_1=\frac{5-6}{-6+5}$

$m_1=\frac{-1}{-1}$

$m_1=1$

If $m_2$ be the slope of the required line and the line is perpendicular;

$m_1\times m_2=-1$

$1\times m_2=-1$

$m_2=-1$

Required equation of line passing through (2,3) is:

$y-y_1=m_2(x-x_1)$

$y-3=-1(x-2)$

$y-3=-x+2$

$x+y-5=0$

$x+y=5$

Option (D) is correct.