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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3911 : Algebra 1

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

Possible Answers:

$\sqrt{28}$

$\sqrt{205}$

$\sqrt{45}$

$\sqrt{19}$

$\sqrt{-9}$

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

Find the length of the line with the following endpoints:

(12,1)(6,4)

Possible Answers:

$3\sqrt{5}$

$\sqrt{47}$

$\sqrt{46}$

$2\sqrt{11}$

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:

$10\sqrt{2}$

$\sqrt{147}$

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 #42 : Points And Distance Formula

Find the length of the line with the following endpoints:

(9,4)(-6,2)

Possible Answers:

$\sqrt{229}$

$\sqrt{227}$

$\sqrt{231}$

$7\sqrt{5}$

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 #43 : Points And Distance Formula

Find the length of the line with the following endpoints:

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

Possible Answers:

$3\sqrt{2}$

$2\sqrt{5}$

$\sqrt{19}$

$\sqrt{17}$

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 #631 : Functions And Lines

Find the length of the line with the following endpoints:

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

Possible Answers:

$2\sqrt{76}$

$\sqrt{178}$

$4\sqrt{89}$

$\sqrt{177}$

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 #45 : Points And Distance Formula

Find the length of the line with the following endpoints:

(1,2)(15,20)

Possible Answers:

$4\sqrt{254}$

$10\sqrt{52}$

$2\sqrt{130}$

$\sqrt{523}$

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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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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Algebra 1 : Equations of Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #3911 : Algebra 1

Example Question #41 : How To Find The Length Of A Line With 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 #42 : Points And Distance Formula

Example Question #43 : Points And Distance Formula

Example Question #631 : Functions And Lines

Example Question #45 : Points And Distance Formula

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

Example Question #3919 : Algebra 1

All Algebra 1 Resources

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