# Distance Formula Practice Problems with Answers

There are ten (10) practice problems here about the **distance formula**. As you work on the different problems, I hope you develop a better understanding of how to use the distance formula.

**Problem 1:** How far is the point [latex]\left( { – 4,6} \right)[/latex] from the origin?

## Answer

[latex]\color{black}2\sqrt {13} [/latex] units

**Problem 2:** Find the distance between the points [latex]\left( {4,7} \right)[/latex] and [latex]\left( {1, – 6} \right)[/latex]. Round your answer to the nearest hundredth.

## Answer

[latex]\color{black}13.34[/latex] units

**Problem 3:** Find the distance between the points on the XY-plane. Round your answer to one decimal place.

## Answer

[latex]\color{black}8.6[/latex] units

**Problem 4:** Determine the distance between points on the coordinate plane. Round your answer to two decimal places.

## Answer

[latex]\color{black}8.06[/latex] units

**Problem 5:** The **chord **of a circle has endpoints as shown below (in green dots). What is the length of the chord?

## Answer

[latex]\color{black}4\sqrt 5[/latex] units

**Problem 6:** The **diameter **of a circle has endpoints as shown below (in red dots). What is the length of the diameter?

## Answer

[latex]\color{black}\sqrt 13[/latex] units

**Problem 7:** Find the two points on the ** x-axis** that are [latex]15[/latex] units away from the point [latex]\left( {-2, 9} \right)[/latex].

## Answer

[latex]\left( {10,0} \right)[/latex] and [latex]\left( { – 14,0} \right)[/latex]

**Problem 8:** Find the two points found on the ** y-axis** which are [latex]25[/latex] units from the point [latex]\left( {7, -5} \right)[/latex].

## Answer

[latex]\left( {0,19} \right)[/latex] and [latex]\left( {0, – 29} \right)[/latex]

**Problem 9:** Find the values of [latex]\color{red}k[/latex] such that the points [latex]\left( {{\color{red}k}, – 1} \right)[/latex] and [latex]\left( {5, 4} \right)[/latex] have a distance of [latex]{13}[/latex] units.

## Answer

[latex]{k_1} = – 7[/latex] and [latex]{k_2} = 17[/latex]

**Problem 10:** Find the values of [latex]\color{red}m[/latex] such that the points [latex]\left( {{\color{red}m},3} \right)[/latex] and [latex]\left( {1,{\color{red}m}} \right)[/latex] are [latex]10[/latex] units apart.

## Answer

[latex]{m_1} = – 5[/latex] and [latex]{m_2} = 9[/latex]

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