Question

Which of the following points does not lie on the line x - 2y + 3 = 0?

• A. (1, 2)
• B. (-5, -1)
• C. (5, 2)
• D. (-7, -2)

Answer 1

The correct option is C (5, 2)

A point lies on a line if its coordinates satisfy the equation of the line.
The equation of the line is x - 2y + 3 = 0

To check if (1, 2) lies on the line substitute x = 1, y = 2 in its equation.
LHS = 1- 2(2) + 3 = 0 = RHS
Therefore, (1, 2) lies on the line
x - 2y + 3 = 0

To check if (-5, -1) lies on the line substitute x = -5, y = -1 in its equation.
LHS = -5 - 2(-1) + 3 = -5 + 2 + 3 = 0
= RHS
Therefore, (-5, -1) lies on the line
x - 2y + 3 = 0

To check if (5, 2) lies on the line substitute x = 5, y = 2 in its equation.
LHS = 5- 2(2) + 3 = 4 $\ne$ 0 = RHS
Therefore, (5, 2) does not lie on the line x - 2y + 3 = 0

To check if (-7, -2) lies on the line substitute x = -7, y = -2 in its equation.
LHS = -7- 2(-2) + 3 = -7 + 4 + 3 = 0
= RHS
Therefore, (-7, -2) lies on the line
x - 2y + 3 = 0