Question

Prove that the line joining the points (2, 1) and (1, 2) and the line joining the points (3, 5) and (4, 7) are not parallel. What are the coordinates of their point of intersection?

Answer 1

Let the given points be A (2, 1), B (1, 2), C (3, 5) and D (4, 7).

Slope of line AB =

Slope of line CD =

⇒ Slope of line AB ≠ Slope of line CD

Therefore, the given lines are not parallel.

Let the point of intersection of both the lines be E (x₁, y₁).

Therefore, the slope of the line BE should be equal to the slope of the line AB.

Slope of line BE =

⇒ y₁ − 2 = −x₁ + 1

⇒ y₁ + x₁ = 3 ….. (1)

Similarly, the slope of the line DE should be equal to the slope of the line CD.

Slope of line DE =

⇒ y₁−7 = 2x₁ − 8

⇒ y₁− 2x₁ = −1 ….. (2)

Solving (1) and (2), we get:

x₁ = , y₁ =

Therefore, the point of intersection of both the lines is