Use distance formula to verify that the points A(0,7) ,B(3,-5) and C(-2,15) are collinear.

Question

use the distance formula

 

Answer 1

The distance formula is:   √((x₂-x₁)² + (y₂-y₁)²)

 

Three points (say, C, A, and B) are collinear if the distance CB = distance CA + distance AB

  (note: in order to form a triangle, the sum of the lengths of two sides must exceed the length of the third side.)

 

Distance CB:  √((-2-3)² + (15-(-5))²)

                    √(25+400)

                     √425

                     5√17

 

Distance CA:   √((-2-0)² + (15-7)²)

                      √(4+64)

                      √68

                      2√17

 

Distance AB:  √((3-0)² + (-5-7)²)

                     √(9+144)

                     √153

                      3√17

 

Does distance CB = distance CA + distance AB    ?

                     5√17 = 2√17  +  3√17

                     5√17 = 5√17    ?  yes, points A, B, and C are collinear.

Answer 2

point A is between point C and point B

point C to point A is...

√[8^2+(-2)^2]=√68

point A to point B is...

√[12^2+(-3)^2]=√153

point C to point B is...

√[20^2+(-5)^2]=√425

√68+√153=√425

8.246+12.369=20.615

20.615=20.615

it would be easier finding the slopes if you did not have to use the distance formula...

8/-2=12/-3=20/-5=-4