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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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10 Diagnostic Tests 557 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : How To Find The Length Of A Line With Distance Formula

$\small (12,20)(2,4)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {192}$

$\small \sqrt {456}$

$\small \sqrt {356}$

$\small \sqrt {35}$

Correct answer:

$\small \sqrt {356}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates.

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small d=\small \sqrt{(12-2)^{2}+(20-4)^{2}} \\ \\ = \sqrt{10^{2}+16^{2}}\\ \\ = \sqrt{100+256} \\ \\= \sqrt {356}$ .

This is the length.

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Example Question #7 : How To Find The Length Of A Line With Distance Formula

$\small (4,6)(10,2)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {203}$

$\small \sqrt {62}$

$\sqrt {52}$

$\small \sqrt {19}$

Correct answer:

$\sqrt {52}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (4,6)(10,2)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small \small d=\small \sqrt{(10-4)^{2}+(2-6)^{2}} \\ \\= \sqrt{6^{2}+(-4)^{2}} \\ \\= \sqrt{36+16} \\ \\= \sqrt {52}$ .

This is the length.

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Example Question #4 : Points And Distance Formula

$\small (4,5)(6,7)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt 8$

$\small 18$

$\small 8$

$\small \sqrt {18}$

Correct answer:

$\small \sqrt 8$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (4,5)(6,7)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small \small \small d=\small \sqrt{(6-4)^{2}+(7-5)^{2}} \\ \\= \sqrt{2^{2}+2^{2}} \\ \\= \sqrt{4+4} \\ \\= \sqrt 8$ .

This is the length.

Report an Error

Example Question #11 : How To Find The Length Of A Line With Distance Formula

$\small (10,4)(5,8)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {40}$

$\small \sqrt {41}$

$\small \sqrt {31}$

$\small \sqrt {11}$

Correct answer:

$\small \sqrt {41}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (10,4)(5,8)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small \small \small \small \small d=\small \sqrt{(10-5)^{2}+(4-8)^{2}} \\ \\= \sqrt{5^{2}+(-4)^{2}} \\ \\= \sqrt{25+16} \\ \\= \sqrt {41}$ .

This is the length.

Report an Error

Example Question #12 : Points And Distance Formula

$\small (12,7)(14,8)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt 5$

$\small \sqrt{13}$

$\small \sqrt {10}$

$\small \sqrt 9$

Correct answer:

$\small \sqrt 5$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (12,7)(14,8)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\d=\small \sqrt{(14-12)^{2}+(8-7)^{2}} \\ \\= \sqrt{2^{2}+1^{2}} \\ \\= \sqrt{4+1} \\ \\= \sqrt 5$ .

This is the length.

Report an Error

Example Question #11 : How To Find The Length Of A Line With Distance Formula

$\small (10,4)(8,2)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {10}$

$\small 12$

$\small \sqrt 8$

$\small \sqrt{12}$

Correct answer:

$\small \sqrt 8$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (10,4)(8,2)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ d=\small \sqrt{(10-8)^{2}+(4-2)^{2}} \\ \\= \sqrt{2^{2}+2^{2}} \\ \\= \sqrt{4+4} \\ \\= \sqrt 8$ .

This is the length.

Report an Error

Example Question #11 : How To Find The Length Of A Line With Distance Formula

$\small (10,4)(6,2)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {20}$

$\small \sqrt {17}$

$\small \sqrt {18}$

$\sqrt {19}$

Correct answer:

$\small \sqrt {20}$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (10,4)(6,2)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ d=\small \sqrt{(10-6)^{2}+(4-2)^{2}} \\ \\= \sqrt{4^{2}+2^{2}} \\ \\= \sqrt{16+4} \\ \\= \sqrt {20}$ .

This is the length.

Report an Error

Example Question #15 : Points And Distance Formula

$\small (14,9)(12,7)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {34}$

$\small \sqrt {10}$

$\small \sqrt 3$

$\small \sqrt 8$

Correct answer:

$\small \sqrt 8$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (14,9)(12,7)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\\small d=\small \sqrt{(14-12)^{2}+(9-7)^{2}} \\ \\= \sqrt{2^{2}+2^{2}} \\ \\= \sqrt{4+4} \\ \\= \sqrt 8$ .

This is the length.

Report an Error

Example Question #11 : Points And Distance Formula

$\small (20,4)(16,7)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {319}$

$\small \sqrt {127}$

Correct answer:

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (20,4)(16,7)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small d=\small \sqrt{(20-16)^{2}+(4-7)^{2}} \\ \\= \sqrt{4^{2}+3^{2}} \\ \\= \sqrt{16+9} \\ \\= \sqrt{25}\\ \\=5$ .

This is the length.

Report an Error

Example Question #12 : Points And Distance Formula

$\small (14,8)(16,7)$

Find the length of the line between the two points provided using the distance formula.

Possible Answers:

$\small \sqrt {10}$

$\small \sqrt{182}$

$\small \sqrt 5$

$\small \sqrt {52}$

Correct answer:

$\small \sqrt 5$

Explanation:

It is definately possible to find the distance from point A to point B, given the coordinates:

$\small (14,8)(16,7)$ .

We can do this by using the formula:

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

The points provided can be plugged into this formula as follows:

$\\ \small d=\small \sqrt{(16-14)^{2}+(7-8)^{2}}\\ \\ = \sqrt{2^{2}+(-1)^{2}} \\ \\= \sqrt{4+1}\\ \\ = \sqrt 5$ .

This is the length.

Report an Error

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Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #6 : How To Find The Length Of A Line With Distance Formula

Example Question #7 : How To Find The Length Of A Line With Distance Formula

Example Question #4 : Points And Distance Formula

Example Question #11 : How To Find The Length Of A Line With Distance Formula

Example Question #12 : Points And Distance Formula

Example Question #11 : How To Find The Length Of A Line With Distance Formula

Example Question #11 : How To Find The Length Of A Line With Distance Formula

Example Question #15 : Points And Distance Formula

Example Question #11 : Points And Distance Formula

Example Question #12 : Points And Distance Formula

All Algebra 1 Resources

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