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.

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

Answer

$\color{red}2\sqrt {13}$ 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.

Answer

$\color{red}13.34$ 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

$\color{red}8.6$ 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

$\color{red}8.06$ units

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

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

Answer

$\color{red}4\sqrt 5$ units

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

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

Answer

$\color{red}\sqrt 13$ units

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

Answer

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

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

Answer

$\left( {0,19} \right)$ 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.

Answer

${k_1} = - 7$ 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.

Answer

${m_1} = - 5$ and ${m_2} = 9$

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