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

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The discussion demonstrates that the points A(-4, 6), B(-1, 2), and C(2, -2) are collinear by using the distance formula to calculate the lengths of segments AB, BC, and AC. The calculations show that AB equals 5, BC equals 5, and AC equals 10. By adding AB and BC, the result equals AC, confirming the equation AB + BC = AC. This proves that the three points lie on the same line. The conclusion validates the initial assertion regarding the relationship between the points.
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Given A(-4, 6), B(-1, 2), and C(2, -2), show that AB + BC = AC.

Can this be done using the distance formula?
 
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Yes, and if this is true, then what must be true of the 3 points?
 
MarkFL said:
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.
 
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
 
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