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Algebra 1 : How to find the length of a line with distance formula

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Example Question #41 : Points And Distance Formula

Find the length of the line with endpoints (-7, 2) and (5, 9) using the distance formula.

Possible Answers:

$\sqrt{193}$

$\sqrt{19}$

$\sqrt{125}$

193

Correct answer:

$\sqrt{193}$

Explanation:

To solve, we will use the distance formula:

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

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

(-7, 2) and (5, 9)

we can substitute into the formula. We get,

$\text{distance} = \sqrt{(5 - - 7)^2 + (9 - 2)^2}$

$\text{distance} = \sqrt{(12)^2 + (7)^2}$

$\text{distance} = \sqrt{144 + 49}$

$\text{distance} = \sqrt{193}$

Therefore, the length of the line with the endpoints (-7, 2) and (5, 9) is $\sqrt{193}$ .

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Example Question #42 : Points And Distance Formula

Given the following two points:

(8,7) (1,5)

Calculate the distance between the two points using the distance formula. Round your answer to one decimal place.

Possible Answers:

7.9

6.8

10.1

8.4

7.3

Correct answer:

7.3

Explanation:

The distance formula equation is as follows:

$d = \sqrt{(x1-x2)^{2} + (y1-y2)^{2}}$

Note that x1,x2,y1, y2 simply refer to the 'first and ' and 'second and ' points, these are simply for keeping track and do not require any further computation.

The and coordinates given can be plugged in to solve for the distance between these two points.

$d = \sqrt{(8-1)^{2} + (7-5)^{2}}$

$d = \sqrt{(7)^{2} + (2)^{2}}$

$d = \sqrt{49 + 4}$

$d = \sqrt{53}$

d = 7.3

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Example Question #43 : Points And Distance Formula

Find the length of the line with the endpoints (0, 5) and (6, 8).

Possible Answers:

$\sqrt{45}$

$\sqrt{28}$

$\sqrt{19}$

$\sqrt{-9}$

$\sqrt{205}$

Correct answer:

$\sqrt{45}$

Explanation:

To find the length of a line, we use the distance formula

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

where (x_1, y_1) and (x_2, y_2) are the endpoints. Knowing this, we can substitute the endpoints into the equation. We get

$\sqrt{(6-0)^2 + (8-5)^2}$

$\sqrt{6^2 + 3^2}$

$\sqrt{36 + 9}$

$\sqrt{45}$

Therefore, the length of the line with the endpoints (0, 5) and (6, 8) is $\sqrt{45}$ .

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Example Question #44 : Points And Distance Formula

Find the length of the line with the following endpoints:

(12,1)(6,4)

Possible Answers:

$2\sqrt{11}$

$\sqrt{46}$

$\sqrt{47}$

$3\sqrt{5}$

Correct answer:

$3\sqrt{5}$

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 (12,1) and (6,4) and solve:

$\sqrt{(12-6)^{2}+(1-4)^{2}}=\sqrt{(6)^{2}+(-3)^{2}}=\sqrt{36+9}=\sqrt{45}=3\sqrt{5}$

This gives a final answer of $3\sqrt{5}$

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Example Question #41 : How To Find The Length Of A Line With Distance Formula

Find the length of the line with the following endpoints:

(15,5)(3,5)

Possible Answers:

$\sqrt{147}$

$10\sqrt{2}$

Correct answer:

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 (15,5) and (3,5) and solve:

$\sqrt{(15-3)^{2}+(5-5)^{2}}=\sqrt{(12)^{2}+(0)^{2}}=\sqrt{144}=12$

This gives a final answer of

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Example Question #46 : Points And Distance Formula

Find the length of the line with the following endpoints:

(-6,-12)(2,7)

Possible Answers:

$5\sqrt{17}$

$\sqrt{427}$

$\sqrt{471}$

$2\sqrt{105}$

Correct answer:

$5\sqrt{17}$

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,-12) and (2,7) and solve:

$\sqrt{(7+12)^{2}+(2+6)^{2}}=\sqrt{(19)^{2}+(8)^{2}}=\sqrt{361+64}=\sqrt{425}=5\sqrt{17}$

This gives a final answer of $5\sqrt{17}$

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Example Question #47 : Points And Distance Formula

Find the length of the line with the following endpoints:

(9,4)(-6,2)

Possible Answers:

$\sqrt{227}$

$\sqrt{229}$

$\sqrt{231}$

$7\sqrt{5}$

Correct answer:

$\sqrt{229}$

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 (9,4) and (-6,2) and solve:

$\sqrt{(9+6)^{2}+(4-2)^{2}}=\sqrt{(15)^{2}+(2)^{2}}=\sqrt{225+4}=\sqrt{229}$

This gives a final answer of $\sqrt{229}$

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Example Question #48 : Points And Distance Formula

Find the length of the line with the following endpoints:

(-7,5)(-4,2)

Possible Answers:

$\sqrt{17}$

$2\sqrt{5}$

$3\sqrt{2}$

$\sqrt{19}$

Correct answer:

$3\sqrt{2}$

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 (-7,5) and (-4,2) and solve:

$\sqrt{(-4+7)^{2}+(2-5)^{2}}=\sqrt{(3)^{2}+(-3)^{2}}=\sqrt{9+9}=\sqrt{18}=3\sqrt{2}$

This gives a final answer of $3\sqrt{2}$

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Example Question #49 : Points And Distance Formula

Find the length of the line with the following endpoints:

(-1,-6)(12,-3)

Possible Answers:

$2\sqrt{76}$

$\sqrt{178}$

$\sqrt{177}$

$4\sqrt{89}$

Correct answer:

$\sqrt{178}$

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 (-1,-6) and (12,-3) and solve:

$\sqrt{(12+1)^{2}+(-3+6)^{2}}=\sqrt{(13)^{2}+(3)^{2}}=\sqrt{169+9}=\sqrt{178}$

This gives a final answer of $\sqrt{178}$

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Example Question #50 : Points And Distance Formula

Find the length of the line with the following endpoints:

(1,2)(15,20)

Possible Answers:

$2\sqrt{130}$

$10\sqrt{52}$

$\sqrt{523}$

$4\sqrt{254}$

Correct answer:

$2\sqrt{130}$

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 (1,2) and (15,20) and solve:

$\sqrt{(15-1)^{2}+(20-2)^{2}}= \sqrt{(14)^{2}+(18)^{2}}= \sqrt{196+324}= \sqrt{520}= 2\sqrt{130}$

This gives a final answer of $2\sqrt{130}$

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Algebra 1 : How to find the length of a line with distance formula

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #41 : Points And Distance Formula

Example Question #42 : Points And Distance Formula

Example Question #43 : Points And Distance Formula

Example Question #44 : Points And Distance Formula

Example Question #41 : How To Find The Length Of A Line With Distance Formula

Example Question #46 : Points And Distance Formula

Example Question #47 : Points And Distance Formula

Example Question #48 : Points And Distance Formula

Example Question #49 : Points And Distance Formula

Example Question #50 : Points And Distance Formula

All Algebra 1 Resources

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