Question

Prove that the point A(2,6) B(4,2) C(7-4) are colliner

Answer 1

Answer:

Step-by-step explanation:

a similar question has similar answer

Let A(0,-2) , B ( 2 , 4 ) and C ( -1 , -5 ) be the given points.

A ( 0 , -2 ) and B ( 2 , 4 )

Here,

X1 = 0 , Y1 = -2 and X2 = 2 , Y2 = 4.

Therefore,

AB = ✓(X2 - X1 )² + ( Y2 - Y1 )²

AB = ✓( 2 - 0 )² + ( 4 + 2 )²

AB = ✓4 + 36

AB = √40 = ✓2 × 2 × 2 × 5

AB = 2√10 units.

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B ( 2 , 4 ) and C ( -1 , - 5 )

Here,

X1 = 2 , Y1 = 4 and X2 = -1 , Y2 = -5.

Therefore,

BC = ✓( X2 - X1 )² + ( Y2 - Y1)²

BC = ✓ ( -1 - 2 )² + ( -5 - 4 )²

BC = ✓9 + 81

BC = ✓90 = ✓2 × 3 × 3 × 5

BC = 3√10 units.

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A ( 0 , -2 ) and C ( -1 , - 5 )

Here,

X1 = 0 , Y1 = -2 and X2 = -1 , Y2 = -5

AC = ✓ ( X2 - X1 )² + ( Y2 - Y1 )²

AC = ✓ ( -1 - 0)² + ( -5 + 2 )²

AC = ✓1 + 9

AC = √10 units.

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AB + AC = 2√10 + √10 = 3√10 units.

And,

BC = 3√10 units.

Thus,

AB + AC = BC.

Hence,

The given points A , B , C are collinear.