Question

Consider the three points `(-2, 4), (1,2) and (4,r )` on the same line. What is the value of `r`?

Answer 1

`0=r`

Explanation:

If two points are on a line, then `(Deltay)/(Deltax)` or `(y_2-y_1)/(x_2-x_1)` is the slope.

Since `(-2,4)(1,2)(4,r)` are on the same line, they share a common slope.

We find the slope between `(-2,4)` and `(1,2)`, which is also the common slope.

`m=(2-4)/(1-(-2))=>m=-2/3`

This means that the slope between the points `(1,2)` and `(4,r)` is `-2/3`

Therefore, we have:

`(r-2)/(4-1)=-2/3`

=>`-2(4-1)=3(r-2)`

=>`-8+2=3r-6`

=>`-6=3r-6`

=>`0=3r`

=>`0=r` That is our answer!