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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