# 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!

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.

${m_1} = – 5$ and ${m_2} = 9$