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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