Answer:
Option C is correct.i.e., ( 6 , 4 ) lie on given line.
Explanation:
Given Equation, y - 4 = -2 ( x - 6 )
Option A:
From given point, x = -6 and y = -4
LHS = y - 4 = -4 - 4 = -8
RHS = -2 ( x - 6 ) = -2 ( -6 - 6 ) = -2 × ( -12 ) = 24
LHS ≠ RHS
⇒ This point does not lie on given line.
Option B:
From given point, x = -4 and y = -6
LHS = y - 4 = -6 - 4 = -10
RHS = -2 ( x - 6 ) = -2 ( -4 - 6 ) = -2 × ( -10 ) = 20
LHS ≠ RHS
⇒ This point does not lie on given line.
Option C:
From given point, x = 6 and y = 4
LHS = y - 4 = 4 - 4 = 0
RHS = -2 ( x - 6 ) = -2 ( 6 - 6 ) = -2 × ( 0 ) = 0
LHS = RHS
⇒ This point lie on given line.
Option D:
From given point, x = 4 and y = 6
LHS = y - 4 = 6 - 4 = 2
RHS = -2 ( x - 6 ) = -2 ( 4 - 6 ) = -2 × ( -2 ) = 4
LHS ≠ RHS
⇒ This point does not lie on given line.
Therefore, Option C is correct.i.e., ( 6 , 4 ) lie on given line.