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Algebra 1 : Points and Distance Formula

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Example Questions

Example Question #51 : How To Find The Length Of A Line With Distance Formula

Find the length of the line with the following endpoints:

(2,1)(7,3)

Possible Answers:

$\sqrt{26}$

$\sqrt{29}$

$2\sqrt{27}$

Correct answer:

$\sqrt{29}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (2,1) and (7,3) and solve:

$\sqrt{(7-2)^{2}+(3-1)^{2}}=\sqrt{(5)^{2}+(2)^{2}}=\sqrt{25+4}=\sqrt{29}$

This gives a final answer of $\sqrt{29}$

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Example Question #3919 : Algebra 1

Find the length of the line with the following endpoints:

(3,-2)(12,9)

Possible Answers:

$10\sqrt{3}$

$10\sqrt{2}$

$\sqrt{202}$

$\sqrt{201}$

Correct answer:

$\sqrt{202}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (3,-2) and (12,9) and solve:

$\sqrt{(12-3)^{2}+(9+2)^{2}}=\sqrt{(9)^{2}+(11)^{2}}=\sqrt{81+121}=\sqrt{202}$

This gives a final answer of $\sqrt{202}$

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Example Question #632 : Functions And Lines

Find the length of the line with the following endpoints:

(6,7)(-6,-7)

Possible Answers:

$\sqrt{337}$

$2\sqrt{85}$

$2\sqrt{87}$

$\sqrt{341}$

Correct answer:

$2\sqrt{85}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (6,7) and (-6,-7) and solve:

$\sqrt{(6+6)^{2}+(7+7)^{2}}=\sqrt{(12)^{2}+(14)^{2}}=\sqrt{144+196}=\sqrt{340}=2\sqrt{85}$

This gives a final answer of $2\sqrt{85}$

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Example Question #51 : Points And Distance Formula

What is the distance of the line connected by the points (2,8) and (-3,6) ?

Possible Answers:

$3\sqrt{5}$

$2\sqrt{5}$

$\sqrt{21}$

$\sqrt{29}$

$\sqrt{31}$

Correct answer:

$\sqrt{29}$

Explanation:

Use the distance formula to determine the line connected by the two points.

The distance formula is:

$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Let:

(x_1,y_1) = (2,8)

(x_2,y_2) =(-3,6)

Substitute the points into the formula.

$d= \sqrt{(-3-2)^2+(6-8)^2}$

Simplify the inner terms.

$d= \sqrt{(-5)^2+(-2)^2}$

$d= \sqrt{25+4} = \sqrt{29}$

The distance of the line connect by the two points is: $\sqrt{29}$

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Example Question #634 : Functions And Lines

Find the length of the line with the following endpoints:

(-5,-3)(4,2)

Possible Answers:

$\sqrt{106}$

$4\sqrt{29}$

$4\sqrt{27}$

$4\sqrt{28}$

Correct answer:

$\sqrt{106}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (-5,-3) and (4,2) and solve:

$\sqrt{(4+5)^{2}+(2+3)^{2}}=\sqrt{(9)^{2}+(5)^{2}}=\sqrt{81+25}=\sqrt{106}$

This gives a final answer of $\sqrt{106}$

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Example Question #635 : Functions And Lines

Find the length of the line with the following endpoints:

(4,9)(-2,-1)

Possible Answers:

$2\sqrt{73}$

$9\sqrt{5}$

$\sqrt{136}$

$\sqrt{147}$

Correct answer:

$\sqrt{136}$

Explanation:

In order to find the distance between two points on a line, use the formula below:

$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$

Plug in the points (4,9) and (-2,-1) and solve:

$\sqrt{(9+1)^{2}+(4+2)^{2}}=\sqrt{(10)^{2}+(6)^{2}}=\sqrt{100+36}=\sqrt{136}$

This gives a final answer of $\sqrt{136}$

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Example Question #3925 : Algebra 1

Find the length of the line between the two points

(1, 5) and (-3, 4)

Possible Answers:

$\sqrt{85}$

$\sqrt{17}$

$\sqrt{3}$

$\sqrt{5}$

$\sqrt{12}$

Correct answer:

$\sqrt{17}$

Explanation:

To find the length between two points, we use the following distance formula:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

where (x_1, y_1) and (x_2, y_2) are the points given.

Using the given points

(1, 5) and (-3, 4)

we can substitute into the formula. We get

$d = \sqrt{(-3-1)^2 + (4-5)^2}$

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

$d = \sqrt{16 + 1}$

$d = \sqrt{17}$

Therefore, the distance between the points (1, 5) and (-3, 4) is $\sqrt{17}$ .

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Example Question #3926 : Algebra 1

Find the length of the line between the points

(-3, -3) and (-5, -8)

Possible Answers:

$\sqrt{7}$

$\sqrt{29}$

$\sqrt{-7}$

$\sqrt{185}$

$\sqrt{37}$

Correct answer:

$\sqrt{29}$

Explanation:

To find the length between two points, we use the following distance formula:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

where (x_1, y_1) and (x_2, y_2) are the points given.

Using the given points

(-3, -3) and (-5, -8)

we can substitute into the formula. We get

$d = \sqrt{(-5 - -3)^2 + (-8 - -3)^2}$

$d = \sqrt{(-5+3)^2 + (-8+3)^2}$

$d = \sqrt{(-2)^2 + (-5)^2}$

$d = \sqrt{4 + 25}$

$d = \sqrt{29}$

Therefore, the distance between the points (-3, -3) and (-5, -8) is $\sqrt{29}$ .

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Example Question #3926 : Algebra 1

If the line $\overline{AB}$ is connected by the points (8,3) and (-3,5) , what is the exact length of this line?

Possible Answers:

$5\sqrt2$

$\sqrt{39}$

$\sqrt{89}$

$5\sqrt5$

$\sqrt{29}$

Correct answer:

$5\sqrt5$

Explanation:

Use the distance formula to determine the distance of this line.

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the points into the equation.

$d=\sqrt{(5-3)^2+(-3-8))^2}$

Simplify the radical.

$d=\sqrt{(2)^2+(-11)^2} = \sqrt{4+121} = \sqrt{125}$

Pull out the common factors. This radical can still be reduced.

$\sqrt{125} = \sqrt{25}\cdot \sqrt5 =5\sqrt5$

The exact length of the line is: $5\sqrt5$

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Example Question #51 : Points And Distance Formula

Steven and Joel are on a massive grid. Steven is located at point (1,2) on the grid and Joel is located at (-1,-2) . How far away from each other are they?

Possible Answers:

None of these

$2\sqrt{5}units$

20units

$5\sqrt{2}units$

3units

Correct answer:

$2\sqrt{5}units$

Explanation:

The distance formula is:

$d= \sqrt{(x_{1}-x_{_{2}})^2+(y_{1}-y_2)^2}$

Plug in these points into the distance formula.

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

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

$d=\sqrt{20}$

Reduce:

$d=\sqrt{4}*\sqrt{5}$

$d=2\sqrt{5}$

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Algebra 1 : Points and Distance Formula

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #51 : How To Find The Length Of A Line With Distance Formula

Example Question #3919 : Algebra 1

Example Question #632 : Functions And Lines

Example Question #51 : Points And Distance Formula

Example Question #634 : Functions And Lines

Example Question #635 : Functions And Lines

Example Question #3925 : Algebra 1

Example Question #3926 : Algebra 1

Example Question #3926 : Algebra 1

Example Question #51 : Points And Distance Formula

All Algebra 1 Resources

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