Question

find y when the points (5, - 4) (3 ,- 1) (1,y) are collinear.

Answer 1

Ans : x = -1

Solution :

We have many different methods to find collinearity of the given three points. Few of them are

Slopes will be equal.

Area formed by that three points ( triangle) would be zero.

Determinent is equal to zero.

Let the given three points be

(a,b), (c,d), (e,f)

Slopes :

(f - d) /(e-c) = (d-b)/(c-a)

Area :

(1/2) × | a (d-f) + c (f-b) + e (b-d)| = 0

Determinent :

| a (d-f) + c (f-b) + e (b-d)| = 0

Let us consider 1st method (slope)

(5-2)/(9-5) = (2- x)/(5-1)

3/4 = (2-x)/4

(3/4) × 4 = 2-x

3 = 2 - x

x = 2-3

x = -1

Answer 2

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