Lesson 3: Midpoint and Distance Formulas

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

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

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)

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)

​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).

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.

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​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.

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)

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: