Therefore, AB + BC = AC, thus proving that the given equation is true.

[mathdad]

Given A(-4, 6), B(-1, 2), and C(2, -2), show that AB + BC = AC.

Can this be done using the distance formula?

 

[MarkFL]

Yes, and if this is true, then what must be true of the 3 points?

 

[mathdad]

Yes, and if this is true, then what must be true of the 3 points?

If this is true, the 3 points are collinear or lie on the same line.

 

[mathdad]

I will solve this question without using MathMagic Lite.

AB = sqrt{(2 - 6)^2 + (-1 + 5)^2}

AB = sqrt{9 + 16}

AB = sqrt{25}

AB = 5

BC = sqrt{2 + 1)^2 + (- 2 - 2)^2}

BC = sqrt{9 + 16}

BC = sqrt{25}

BC = 5

AC = sqrt{(6)^2 + (-8)^2}

AC = sqrt{36 + 64}

AC = sqrt{100}

AC = 10

AB + BC = AC

5 + 5 = 10

10 = 10