Question

Given points A(4, –2), B(1, 2), C(–2, 6). Find the distance between each two of them. Prove that points A, B, and C are collinear. Which point is in between the other two?

Answer 1

Part 1)
`dAB=5\ units`

Part 2)
`dBC=5\ units`

Part 3)
`dAC=10\ units`

Part 4) In the explanation (The point B is between point A and point C)

Explanation:

we know that

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

`A(4, -2), B(1, 2), C(-2, 6)`

step 1

Find distance AB

`A(4, -2), B(1, 2)`

substitute the values in the formula

`d=\sqrt{(2+2)^(2)+(1-4)^(2)}`

`d=√(25)`

`dAB=5\ units`

step 2

Find distance BC

`B(1, 2), C(-2, 6)`

substitute the values in the formula

`d=\sqrt{(6-2)^(2)+(-2-1)^(2)}`

`d=√(25)`

`dBC=5\ units`

step 3

Find distance AC

`A(4, -2),C(-2, 6)`

substitute the values in the formula

`d=\sqrt{(6+2)^(2)+(-2-4)^(2)}`

`d=√(100)`

`dAC=10\ units`

step 4

Prove that points A, B, and C are collinear. Which point is in between the other two?

we know that

If the points are collinear

then

`AC=AB+BC`

we have

`dAB=5\ units`

`dBC=5\ units`

`dAC=10\ units`

substitute

`10=5+5`

`10=10` ----> is verified

The point B is between point A and point C