Mathematics: 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?

-3/16Step-by-step explanation:Hope it helps you!...

Given points a(4, –2), b(1, 2), c(–2, 6). find the

Ответ:

heids17043

02.01.2022

Mathematics

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)

Step-by-step 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

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

$d=\sqrt{25}$

$dAB=5\ units$

step 2

Find distance BC

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

substitute the values in the formula

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

$d=\sqrt{25}$

$dBC=5\ units$

step 3

Find distance AC

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

substitute the values in the formula

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

$d=\sqrt{100}$

$dAC=10\ units$

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

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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?

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