Given:
The pairs of points are:
a. A(-6,-4), B(-3,-1)
b. C(3.5,1), D(-4,2.5)
c. X(5,-5), Y(-5,5)
To find:
The distance between the pair of points by using the distance formula.
Solution:
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
a.
Using the distance formula, the distance between the points A(-6,-4) and B(-3,-1) is:
[tex]AB=\sqrt{(-3-(-6))^2+((-1-(-4))^2}[/tex]
[tex]AB=\sqrt{(3)^2+(3)^2}[/tex]
[tex]AB=\sqrt{2(3)^2}[/tex]
[tex]AB=3\sqrt{2}[/tex]
[tex]AB\approx 4.2[/tex]
Therefore, the distance between the points A(-6,-4) and B(-3,-1) is about 4.2 units.
b.
Using the distance formula, the distance between the points C(3.5,1) and D(-4,2.5) is:
[tex]CD=\sqrt{(-4-3.5)^2+(2.5-1)^2}[/tex]
[tex]CD=\sqrt{(-7.5)^2+(1.5)^2}[/tex]
[tex]CD=\sqrt{56.25+2.25
}[/tex]
[tex]CD=\sqrt{58.5
}[/tex]
[tex]CD\approx 7.6[/tex]
Therefore, the distance between the points C(3.5,1) and D(-4,2.5) is about 7.6 units.
c.
Using the distance formula, the distance between the points X(5,-5) and Y(-5,5) is:
[tex]XY=\sqrt{(-5-5)^2+(5-(-5))^2}[/tex]
[tex]XY=\sqrt{(-10)^2+(10)^2}[/tex]
[tex]XY=\sqrt{100+100}[/tex]
[tex]XY=\sqrt{200}[/tex]
[tex]XY\approx 14.1[/tex]
Therefore, the distance between the points X(5,-5) and Y(-5,5) is about 14.1 units.
