Check the points (-1-3).(-4,7) and (2.-13) are
Answers
Appropriate question:
Check whether the given coordinates are collinear or not.
Solution:
Before solving the question, we should be aware about the method to check whether given coordinates are collinear or not.
Two very common methods to check whether coordinates are collinear are listed below:
- Find the area of the triangle formed and if the area = 0, this implies that coordinates are collinear.
- Find the slope of the line joining any two common pairs of coordinates, if the slope is same this will imply that the coordinates are collinear.
We will use the concept of area of triangle to solve the given problem.
Area of the triangle formed by the coordinates (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by the following formula:
- Area = 1/2 [x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)
Let's assume the given coordinates be:
- (x₁, y₁) = (-1, -3)
- (x₂, y₂) = (-4, 7)
- (x₃, y₃) = (2, -13)
By using this formula, the area of the triangle formed by given coordinates is given by:
⇒ 1/2 [-1(7 - {-13}) - 4(-13 - {-3}) + 2(-3 - 7)]
⇒ 1/2 [-1(7 + 13) - 4 ( -13 + 3) + 2(-10) ]
⇒ 1/2 [-1(20) - 4(-10) -20 ]
⇒ 1/2 [-20 + 40 - 20 ]
⇒ 1/2 [0]
⇒ 0
Hence the given coordinates are collinear.