Use the Distance Formula to find the distance between each pair of points. Round to the nearest tenth if necessary.
5. P(1, 1), Q(–1, –1)














6. E(1/2,4 1/4),F(5,-1/2)

Answers

Answer 1

Given:

The pair of points.

5. P(1, 1), Q(–1, –1)

6. [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex]

To find:

The distance between the pair of points.

Solution:

Distance formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

5.

The distance between the pair of points P(1, 1) and Q(–1, –1) is:

[tex]PQ=\sqrt{(-1-1)^2+(-1-1)^2}[/tex]

[tex]PQ=\sqrt{(-2)^2+(-2)^2}[/tex]

[tex]PQ=\sqrt{4+4}[/tex]

[tex]PQ=\sqrt{8}[/tex]

[tex]PQ=2\sqrt{2}[/tex]

Therefore, the distance between P and Q is [tex]2\sqrt{2}[/tex].

6.

The distance between the pair of point [tex]E\left(\dfrac{1}{2},4\dfrac{1}{4}\right), F\left(5,-\dfrac{1}{2}\right)[/tex] is:

[tex]EF=\sqrt{\left(5-\dfrac{1}{2}\right)^2+\left(-\dfrac{1}{2}-4\dfrac{1}{4}\right)^2}[/tex]

[tex]EF=\sqrt{\left(\dfrac{10-1}{2}\right)^2+\left(-\dfrac{1}{2}-\dfrac{17}{4}\right)^2}[/tex]

[tex]EF=\sqrt{\left(\dfrac{9}{2}\right)^2+\left(\dfrac{-2-17}{4}\right)^2}[/tex]

[tex]EF=\sqrt{\dfrac{81}{4}+\left(\dfrac{-19}{4}\right)^2}[/tex]

On further simplification, we get

[tex]EF=\sqrt{\dfrac{81}{4}+\dfrac{361}{16}}[/tex]

[tex]EF=\sqrt{\dfrac{324+361}{16}}[/tex]

[tex]EF=\sqrt{\dfrac{685}{16}}[/tex]

[tex]EF=\sqrt{42.8125 }[/tex]

[tex]EF\approx 6.5[/tex]

Therefore, the distance between E and F is 6.5 units.


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