Find the value of m if the points (5, 1), (–2, –3) and (8, 2m ) are collinear
Solution:
Given, the points (5, 1) (-2, -3) and (8, 2m) are collinear.
We have to find the value of m.
The area of a triangle with vertices A (x₁ , y₁) , B (x₂ , y₂) and C (x₃ , y₃) is
1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
To check for the points to be collinear, the area of the triangle must be zero.
Here, (x₁ , y₁) = (5, 1), (x₂ , y₂) = (-2, -3) and (x₃ , y₃) = (8, 2m)
Area of triangle = 1/2[5(-3 - 2m) + -2(2m - 1) + 8(1 - (-3))] = 0
-15 - 10m - 4m + 2 + 8(4) = 0
-13 - 14m + 32 = 0
-14m + 19 = 0
14m = 19
m = 19/14
Therefore, the value of m is 19/14.
✦ Try This: Determine if the points (0, 4), (0, 4) and (5, 6) are collinear.
Given, the points are (0, 4) (0, 4) and (5, 6)
The area of a triangle with vertices A (x₁ , y₁) , B (x₂ , y₂) and C (x₃ , y₃) is
1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]
To check for the points to be collinear, the area of the triangle must be zero.
Area of triangle = 1/2[0(4 - 6) + 0(6 - 4) + 5(4 - 4)
= 1/2[0 + 0 + 5(0)]
= 0
Area of triangle = 0
Therefore, the given points are collinear.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7
NCERT Exemplar Class 10 Maths Exercise 7.3 Problem 7
Find the value of m if the points (5, 1), (–2, –3) and (8, 2m ) are collinear
Summary:
The value of m if the points (5, 1), (–2, –3) and (8, 2m ) are collinear is 19/14
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