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Algebra 1 : Points and Distance Formula

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 #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.

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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.

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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.

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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.

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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.

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Example Question #18 : Points And Distance Formula

$\small (20,38)(16,28)$

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

Possible Answers:

$\small \sqrt {116}$

$\small \sqrt {12}$

$\small \sqrt {39}$

$\small \sqrt {189}$

Correct answer:

$\small \sqrt {116}$

Explanation:

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

$\small (20,38)(16,28)$ .

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:

$\\ \small d=\small \sqrt{(20-16)^{2}+(38-28)^{2}} \\ \\= \sqrt{4^{2}+(10)^{2}} \\ \\= \sqrt{16+100} \\ \\= \sqrt {116}$ .

This is the length.

Report an Error

Example Question #19 : Points And Distance Formula

$\small (10,4)(14,9)$

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

Possible Answers:

$\small \sqrt {41}$

$\small \sqrt {10}$

$\small \sqrt {49}$

$\small \sqrt {44}$

Correct answer:

$\small \sqrt {41}$

Explanation:

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

$\small (10,4)(14,9)$

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:

$\\ \small d=\small \sqrt{(14-10)^{2}+(9-4)^{2}} \\ \\= \sqrt{4^{2}+5^{2}} \\ \\= \sqrt{16+25}\\ \\ = \sqrt {41}$ .

This is the length.

Report an Error

Example Question #20 : Points And Distance Formula

You have to walk from the grocery store north blocks then west blocks. How far will you be from your original position? (1 block=0.25 miles)

Possible Answers:

$2\ miles$

$7\ miles$

$1.95\ miles$

$15.25\ miles$

$4\ miles$

Correct answer:

$1.95\ miles$

Explanation:

If the student is a visual learner they could draw out a journey of 5 units north then 6 units west. To find the distance between the original and final points they could draw a line connecting the two.

This would ultimately create a right triangle. To find the final distance you could use the Pythagorean Theorem. The longest side length is opposite of the largest angle, which is degrees.

a^2+b^2=c^2

5^2+6^2=c^2

c^2=61

$\sqrt{61}=7.81$ blocks

But the answer must be in the format of distance in miles. So we convert blocks to miles.

$\frac{1block}{0.25 miles}=\frac{7.81blocks}{x miles}$

$x \cdot 1 = 0.25 \cdot 7.81$

x=1.95 miles

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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 #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

Example Question #18 : Points And Distance Formula

Example Question #19 : Points And Distance Formula

Example Question #20 : Points And Distance Formula

All Algebra 1 Resources

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