Answer:
Part 1) [tex]dAB=5\ units[/tex]
Part 2) [tex]dBC=5\ units[/tex]
Part 3) [tex]dAC=10\ units[/tex]
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
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(4, -2), B(1, 2), C(-2, 6)[/tex]
step 1
Find distance AB
[tex]A(4, -2), B(1, 2)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(2+2)^{2}+(1-4)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dAB=5\ units[/tex]
step 2
Find distance BC
[tex]B(1, 2), C(-2, 6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6-2)^{2}+(-2-1)^{2}}[/tex]
[tex]d=\sqrt{25}[/tex]
[tex]dBC=5\ units[/tex]
step 3
Find distance AC
[tex]A(4, -2),C(-2, 6)[/tex]
substitute the values in the formula
[tex]d=\sqrt{(6+2)^{2}+(-2-4)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]dAC=10\ units[/tex]
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
[tex]AC=AB+BC[/tex]
we have
[tex]dAB=5\ units[/tex]
[tex]dBC=5\ units[/tex]
[tex]dAC=10\ units[/tex]
substitute
[tex]10=5+5[/tex]
[tex]10=10[/tex] ----> is verified
The point B is between point A and point C
