# 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 \left( { - 4,6} \right) from the origin?

\color{black}2\sqrt {13} units

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

\color{black}13.34 units

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

\color{black}8.6 units

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

\color{black}8.06 units

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

\color{black}4\sqrt 5 units

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

\color{black}\sqrt 13 units

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

\left( {10,0} \right) and \left( { - 14,0} \right)

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

\left( {0,19} \right) and \left( {0, - 29} \right)

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

{k_1} = - 7 and {k_2} = 17

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