Question

Does the line joining (2, 3) and (3, 1) pass through the point (5, 6)? What about (5, −9)?

Answer 1

Let the given points be A (2, 3), B (3, −1) and C (5, 6).

For a line joining the points A and B to pass through the point C, the slope of the line BC must be equal to the slope of line AC.

Slope of line BC =

Slope of line AC =

⇒ Slope of line BC ≠ Slope of line AC

Therefore, the line joining the points (2, 3) and (3, −1) does not pass through the point (5, 6).

Now, consider the point D (5, −9).

For a line joining the points A and B to pass through the point D, the slope of the line BD must be equal to slope of line AD.

Slope of line BD =

Slope of line AD =

⇒ Slope of line BD = Slope of line AD

Therefore, the line joining the points (2, 3) and (3, −1) passes through the point (5, −9).