Question

If the signs of the coordinates of collinear points P(-6,-2), Q(-5,2), and R (-4,6) reversed, are the 3 new points still collinear?

Answer 1

The new points also collinear.

Explanation:

The given points are P(-6,-2), Q(-5,2), and R (-4,6) are collinear.

If three point are collinear, then

`x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0`

If the signs of the coordinates of collinear points P(-6,-2), Q(-5,2), and R (-4,6) reversed, then the new coordinates are P'(6,2), Q'(5,-2), and R'(4,-6)

Using the formula, check whether the new points are collinear or not.

`6(-2-(-6))+5(-6-2)+4(2-(-2))=0`

`6(-2+6)+5(-8)+4(2+2)=0`

`6(4)+5(-8)+4(4)=0`

`24-40+16=0`

`0=0`

Since LHS=RHS, therefore the new points are collinear.

Answer 2

If all the points have the signs reversed, therefore this means that the whole line is reflected about an axis. Since all are reflected therefore this further means that the new points are still collinear.

We can prove this by plotting the points:

P’(6,2), Q(5,-2), R(4,-6)

From the graph, they are in 1 line hence collinear.