Distance Formula Practice Problems with Answers

Here are ten (10) practice exercises about the distance formula. As you engage with these problems, my hope is that you gain a deeper understanding of how to apply the distance formula. Good luck!

the distance between points A and B is the square root of the of the sum of the difference of the x coordinates and the difference of the y coordinates

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.

two points on the xy-plane. these points are (-4,2) and (3,-3).
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.

two points on the coordinate plane. the points are (0,3) and (-4,-4).
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?

a chord of a circle with endpoints (-2,1) and (-10,5)
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?

a circle with a diameter having endpoints (2,-1) and (4,2)
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]

You may also be interested in these related math lessons or tutorials:

Distance Formula

Distance between Point and Line Formula