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Algebra 1 : Points and Distance Formula

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #3881 : Algebra 1

A line segment stretches from (1,2) to (6,3) . What is the exact distance of this line?

Possible Answers:

$\sqrt{26}$

5.2

$\sqrt{27}$

5.1

None of these answers.

Correct answer:

$\sqrt{26}$

Explanation:

We can find the exact distance between two points by using the distance formula: $D=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$ .

$D=\sqrt{(6-1)^2+(3-2)^2}$

$D=\sqrt{(5)^2+(1)^2}$

$D=\sqrt{26}$

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Example Question #3882 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(2,1) and (12,6)

Possible Answers:

$4\sqrt{5}$

$5\sqrt{5}$

$\sqrt{123}$

$\sqrt{127}$

Correct answer:

$5\sqrt{5}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(12,6) and (x_2,y_2)=(2,1)

$d=\sqrt{(12-2)^{2}+(6-1)^{2}}$

$d=\sqrt{10^{2}+5^{2}}$

$d=\sqrt{100+25}=\sqrt{125}=5\sqrt{5}$

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Example Question #3891 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(10,2) and (5,6)

Possible Answers:

$\sqrt{40}$

$\sqrt{43}$

$\sqrt{42}$

$\sqrt{41}$

Correct answer:

$\sqrt{41}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(10,2) and (x_2,y_2)=(5,6)

$d=\sqrt{(10-5)^{2}+(2-6)^{2}}$

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

$d=\sqrt{25+16}=\sqrt{41}$

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Example Question #3892 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(13,15) and (6,3)

Possible Answers:

$\sqrt{189}$

$\sqrt{193}$

$\sqrt{191}$

Correct answer:

$\sqrt{193}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(13,15) and (x_2,y_2)=(6,3)

$d=\sqrt{(13-6)^{2}+(15-3)^{2}}$

$d=\sqrt{7^{2}+12^{2}}$

$d=\sqrt{49+144}=\sqrt{193}$

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Example Question #3893 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(-2,-1) and (1,-3)

Possible Answers:

$\sqrt{14}$

$2\sqrt{3}$

$\sqrt{13}$

Correct answer:

$\sqrt{13}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(1,-3) and (x_2,y_2)=(-2,-1)

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

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

$d=\sqrt{9+4}=\sqrt{13}$

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Example Question #3894 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(-5,-3) and (1,-2)

Possible Answers:

$\sqrt{35}$

$\sqrt{39}$

$\sqrt{37}$

Correct answer:

$\sqrt{37}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(1,-2) and (x_2,y_2)=(-5,-3)

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

$d=\sqrt{6^{2}+1^{2}}$

$d=\sqrt{36+1}=\sqrt{37}$

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Example Question #3895 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(-3,-2) and (2,3)

Possible Answers:

$5\sqrt{5}$

$\sqrt{51}$

$5\sqrt{2}$

Correct answer:

$5\sqrt{2}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(-3,-2) and (x_2,y_2)=(2,3)

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

$d=\sqrt{5^{2}+5^{2}}$

$d=\sqrt{25+25}=\sqrt{50}=5\sqrt{2}$

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Example Question #3896 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(2,6) and (5,1)

Possible Answers:

$3\sqrt{5}$

$\sqrt{35}$

$\sqrt{34}$

Correct answer:

$\sqrt{34}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(2,6) and (x_2,y_2)=(5,1)

$d=\sqrt{(5-2)^{2}+(1-6)^{2}}$

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

$d=\sqrt{9+25}=\sqrt{34}$

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Example Question #611 : Functions And Lines

Find the length of the line connecting the following two points. Simplify your answer.

(6,10) and (4,7)

Possible Answers:

$2\sqrt{3}$

$\sqrt{14}$

$\sqrt{13}$

$2\sqrt{5}$

Correct answer:

$\sqrt{13}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(6,10) and (x_2,y_2)=(4,7)

$d=\sqrt{(6-4)^{2}+(10-7)^{2}}$

$d=\sqrt{2^{2}+3^{2}}$

$d=\sqrt{4+9}=\sqrt{13}$

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Example Question #3898 : Algebra 1

Find the length of the line connecting the following two points. Simplify your answer.

(6,2) and (3,8)

Possible Answers:

$2\sqrt{11}$

$2\sqrt{5}$

$3\sqrt{5}$

$2\sqrt{3}$

Correct answer:

$3\sqrt{5}$

Explanation:

To solve this problem we need to remember the distance formula for points on a coordinate plane:

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

In this case, (x_1,y_1)=(6,2) and (x_2,y_2)=(3,8)

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

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

$d=\sqrt{9+36}=\sqrt{45}=3\sqrt{5}$

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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 #3881 : Algebra 1

Example Question #3882 : Algebra 1

Example Question #3891 : Algebra 1

Example Question #3892 : Algebra 1

Example Question #3893 : Algebra 1

Example Question #3894 : Algebra 1

Example Question #3895 : Algebra 1

Example Question #3896 : Algebra 1

Example Question #611 : Functions And Lines

Example Question #3898 : Algebra 1

All Algebra 1 Resources

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