# Midpoint and distance formula worksheet (with answer key)

In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid of both the segment and of the endpoints. Distance is the length of the line segment between any two points on a coordinate plane. Use this math worksheet to find the midpoint and distance between any two points on a coordinate plane.

## What is the “Midpoint and distance formula worksheet?

Midpoint and distance formula worksheet with answers is a math worksheet designed to help learners activate prior knowledge, understand the lesson, and practice their learned skills through a mix of math drills,  reflection and evaluation, and a challenge that will help them construct their own word problem and solve it.

This worksheet will help you better understand the concepts of midpoint and distance formula.

## Instructions on how to use this “Midpoint and distance formula worksheet”

Use this math worksheet to carefully study the basic concept of midpoint and distance formula. Some examples and a real-life problem-solving scenario is also given to help the learner understand how this math concept is being used in daily life. A 3-item activity is given after the lesson in order to exercise the learned concept.

Towards the end of this worksheet, a reflective section is provided in order to help the learner think about their own thinking and assess how they performed in the lesson.

Lastly, it also challenges the learner to devise his/her own method.

## Conclusion

In this worksheet, you will learn about how to find the midpoint and distance between two points in the coordinate plane, and to find the missing coordinate of a point given the midpoint or distance from another known point

## Midpoint and distance formula worksheet (with answer key)

Let’s review the definitions of the midpoint and distance formula.

Midpoint: A midpoint is the center of a line segment, that is, the point on the line segment at the same distance from the end points. The midpoint of the line segment between points and is the point in a coordinate plane.

Distance formula: The distance between two points in a coordinate plane is the length of the line segment between them. The distance between two points can be calculated using the formula:

Example 1: Finding the midpoint between two points.

Let’s find the midpoint between the points A and B.

Step 1: Identify the coordinates of the two points.

For point A, we see that and .

For point B, we see that and .

Step 2: Apply the midpoint formula.

Recalling the midpoint formula of two points, the midpoint between points A

and B is:

Example 2: Finding the endpoint of the line segment given the midpoint and the other endpoint.

Let’s find the endpoint of the line segment having midpoint M and the

other endpoint A.

Step 1: Identify the coordinates of the known point and the midpoint.

For the endpoint A, we set and .

For the midpoint M, we set and .

Step 2: Identify the unknown endpoint.

We need to find the other endpoint B.

Step 3: Apply the midpoint formula and solve for the unknown endpoint.

Recalling the midpoint formula for two points, we can set

This gives us the following two equations for the coordinates of the midpoint

and

Substitute the coordinates of the midpoint and the known point.

and

Solve these two equations for the coordinates of the unknown endpoint B.

B= .

Example 3: Finding the distance between two points.

Let’s find the distance between two points A and B.

Step 1: Identify the coordinates of the endpoints.

For point A, we see that and .

For point B, we see that and .

Step 2: Apply the distance formula.

Recalling the distance formula between two points, the distance between points

A and B is:

Real life problem:

Maryville is located at the coordinates and Silly town is located at . Blaxberg is located midway between Maryville and Silly town. What is the distance from Maryville to Blaxberg?

Since Blaxberg is midway between Maryville and Silly town, find the midpoint of

the coordinates of Maryville and Silly town using the midpoint formula

Blaxberg is located at .

Now, the distance from Maryville to Blaxberg is the distance between the points

and . Applying the distance formula

The distance from Maryville to Blaxberg is 3 units.

## Midpoint and distance formula worksheet (with answer key)

Applying:

1- Find the midpoint and distance between each pair of points.

2- Given the midpoint and an endpoint . Find the other endpoint .

3- John is walking in a straight line on the beach. After two hours of making no turns and traveling at a steady speed, John is two miles east and four miles north of his starting point. How far did John walk? [Hint: Assume that John’s starting point is the origin ].