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Question
Show that the points (1, 3), (2, 1) and `(1/2, 4)` are collinear, by using a straight line
Solution
Let the given points be A (1 , 3), B (2 , 1) and `"C"(1/2, 4)`
Using a straight line
A(1, 3), B(2, 1), `"C"(1/2, 4)`
The equation of the straight line joining the points
A(1, 3), B(2, 1) is
`(x - 1)/(2 - 1) = (y - 3)/(1 - 3)`
`(x - 1)/1 = (y - 3)/(- 2)`
– 2(x – 1) = y – 3
– 2x + 2 = y – 3
2x + y – 2 – 3 = 0
2x + y – 5 = 0 .......(2)
Substituting the third point `"C"(1/2, 4)` in equation (2)
We have `2(1/2) + 4 - 5` = 0
1 + 4 – 5 = 0
0 = 0
∴ The third point `"C"(1/2, 4)` lies on the straight line AB.
Hence the points A, B, C are collinear.
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