Question

prove that the point (4,-5),(1,1) and(-2,7) are collinear ( by distance formula)​

Answer 1

Answer:-Distance formula is

rootover( x2-x1)^2+(y2-y1)^2.

Given points are A = (4,-5)

B = (1,1)

C = (-2,7).

1. Distance between AandB

A =(4,-5) = (x1,y1) & B = (1,1) = (x2,y2).

= rootover(x2-x1)^2+(y2-y1)^2

= rootover(1-4)^2+(1-(-5))^2

= rootover(-3)^2+(6)^2

= rootover9+36

= rootover45.

2. Distance between BandC

B = (1,1) = (x1,y1) & C = (-2,7) = (x2,y2).

=rootover(x2-x1)^2+(y2-y1)^2

= rootover(-2-1)^2+(7-1)^2

= rootover(-3)^2+(6)^2

= rootover9+36

= rootover45.

3. Distance between C and A

C = (-2,7) = (x1,y1) & A = (4,-5) = (x2,y2).

= rootover(x2-x1)^2+(y2-y1)^2

= rootover(4-(-2))^2+(-5-7)^2

= rootover(6)^2+(-12)^2

= rootover36+144

= rootover180

Distance between A and B = Distance between B and C not equal Distance between C and A.

Therefore this three points are not collinear.

I hope it is helps to you.

Answer 2

Answer:

A,B and C are not collinear point.