Question

find the value of 'a' if the points (a,3)(6,-2) (-3,4) are collinear

Answer 1

the value of a is two

Answer 2

hiii! folk.................

A(a,3), B(6,-2),C(-3,4)
A____________B______________ C

By using distance formula

AB=√(6-a)^2+(-2-3)^2

AB=√(61+a^2-12a)-----------_1)

Now,
BC lenght.by distance formula,

BC=√(6+3)^2+(-4-2)

BC=√9^2+(-6^2)

=)√81+36

BC=√117.------------2)

And finally ,we will find length of AC.

AC=√(-3-a)^2+(3-4)^2

AC=√9+a^2+6a+1

AC=√10+a^2+6a----------3)

As you know that when a line is collinier
then follow

★AC=AB+BC

so,Acording to above ....statement.
it may AC^2=AB^2+BC^2

from 1) 2)and 3 we get.

so,. √(10+a^2+6a)^2=√(61+-12aa^2)^2+√(117)^2

=)10+a^2+6a=61+a^2-6a+117

=)12a=168

=)a=168/12

=)a=14.Answer........

Hope it help you......☺

@rajukumar☺☺1☺☺