Lesson 3: Midpoint and Distance Formulas

Lesson 3: Midpoint and Distance Formulas

How to find the exact middle of a segment and the distance between two points

​The Midpoint Formula

We use the midpoint formula in order to find the coordinates of the point that is exactly between two points.​

​

​In the formula, the part finds the x coordinate of the midpoint and the part finds the y coordinate of the midpoint.

​Practice Problems

1) Find the midpoint of (-3, 0) and (1, 8)

2) ​Find the midpoint of (7, 10) and (-5, 11)

3) ​Find the midpoint of (-2, 5) and (6, -5)

​Practice Problems

1) Find the midpoint of (-3, 0) and (1, 8)

​ Answer: (-1, 4)

2) ​Find the midpoint of (7, 10) and (-5, 11)

Answer: (1, 1/2)​

3) ​Find the midpoint of (-2, 5) and (6, -5)

​ Answer: (2, 0)

Multiple Choice

Which of the following points is the midpoint of (2, 5) and (6, 13)?

• (4, 9)

• (3, 7)

• (5, 8)

• (7, 12)

Multiple Choice

Which of the following points is the midpoint of (-3, 2) and (1, -6)?

• (-1, -2)

• (0, -3)

• (-2, -2)

• (0, -4)

​Simplifying Radicals

​Sometimes, when dealing with square roots of numbers which are not perfect squares, mathematicians will simplify the radical instead of providing a decimal or fraction answer.

​

​We can simplify radicals using

​the prime factorization of the radicand (the number under the

​square root symbol).

​Distance Formula

We use the distance formula in order to find the length of a line segment or the distance between two points on the Cartesian Plane.

​

​In the example to the right, the two points are (-3, 2) and (3, 5). We will only get a single number for this answer because it is length, not a coordinate.

​Practice Problems:

1) Find the distance between (2, 5) and (4, 3)

2) Find the distance between (1, 7) and (6, 0)

3) ​Find the distance between (-3, 9) and (5, 4)

​Practice Problems:

1) Find the distance between (2, 5) and (4, 3)

​ Answer:

2) Find the distance between (1, 7) and (6, 0)

​ Answer:

3) ​Find the distance between (-3, 9) and (5, 4)

​ Answer:

Multiple Choice

What is the distance between (8, -3) and (0, 3)?

• 10

• $$5\sqrt[]{25}$$  

• $$5\sqrt[]{5}$$  

• $$\sqrt[]{100}$$  

Multiple Choice

What is the distance between (-3, 1) and (4, 2)?

• $$5\sqrt[]{2}$$  

• $$\sqrt[]{50}$$  

• $$25\sqrt[]{2}$$  

• $$10\sqrt[]{5}$$