Question 2 (i) - Area of Triangle when coordinates are given - Chapter 7 Class 10 Coordinate Geometry

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Ex 7.3 , 2
In each of the following find the value of ‘k’, for which the points are collinear.
(7, –2), (5, 1), (3, k)
Let the given points be A (7, −2), B (5, 1), C (3, k)
If the above points are collinear,
they will lie on the same line,
i.e. the will not form triangle
or We can say that
Area of ∆ABC = 0
1/2 [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = 0
Here
x1 = 7, y1 = −2
x2 = 5, y2 = 1
x3 = 3, y3 = k
Putting values
1/2 [7(1 − k) + 5(k – (−2)) + 3(−2 − 1)] = 0
7(1 − k) + 5(k +2) + 3(−3) = 0 × 2
7 – 7k + 5k + 10 – 9 = 0
– 7k + 5k = − 10 + 9 – 7
−2k = −8
−2k = −8
k = (−8)/(−2)
k = 4

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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