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

Correct option is A

Given:

Point 1: (2, 3)

Point 2: (-5, 6)

Point 3: (-6, 5)

Formula Used:

​​Slope of a line: m =$$\frac{(y_2 - y_1) }{(x_2 - x_1)}$$​

Slope of a line perpendicular to another line: m₁m₂= -1 

Equation of a line in slope-intercept form: y = mx + c

Solution:

Calculate the slope (m1) of the line joining Point 2 and Point 3: m₁=  $$\frac{(5 - 6) }{ (-6 - (-5)) }$$​= 1

Calculate the slope (m2) of the line perpendicular to the line joining Point 2 and Point 3: m₂ = $$\frac{-1 }{ m_1}$$​  = $$\frac{-1}{1}$$=-1​

Calculate the equation of the line passing through Point 1 with slope m₂: 

y - 3 = -1 $$\times$$​ (x - 2)

y - 3 = -x + 2

x + y -5=0

Therefore, the equation of the line passing through (2, 3) and perpendicular to the line joining (-5, 6) and (-6, 5) is: x + y -5=0

Option (c) is right answer.