Question

Using distance formula, verify that the points (1, -1), (5, 2) and (9, 5) are collinear or not ?​

Answer 1

Answer:

Yes they are collinear.

Step-by-step explanation:

LET (1,-1) BE POINT "A" , (5,2) BE POINT "B" , (9,5) BE POINT "C".

Distance formula = root ( x2-x1)*2 + root over (y2-y1) *2

So,

Distance of points (1,-1) and (5,2) is

root over (5-1)*2+root over (2+1)*2

=> root over (4*2+3*2)

=> root over (16+9)

=> root over (25) = 5.

Distance of points (5,2) and (9,5) is

root over (9-5)*2+root over (5-2)*2

=> root over (4*2+3*2)

=> root over (16+9)

=> root over (25) = 5.

Distance of points (9,5) and (1,-1) is

root over (1-9)*2+root over (-1-5)*2

=> root over (8*2+(-6)*2)

=> root over (64+36)

=> root over (100) = 10.

IF A LINE IS IN COLLINEAR THEN AB +BC SHOULD BE EQUAL TO AC

So,

AB +BC =AC

5+5 =10

SO POINTS THREE REPRESENTS A COLLINEAR LINE.

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