Midpoints Algebra

Locating Points and Midpoints 

FMS Geometry Honors
Mr. Geraldo Banaag
September 1, 2020

Multiple Choice

Warm it up!

Find the distance between the points (-5, 2) and (3, 6).

• $$\sqrt{20}$$  

• $$\sqrt{80}$$  

• $$\sqrt{68}$$  

Multiple Select

Which of the following shows the distance formula?

• $$d\ =\ \sqrt{\left(x_1\ +\ x_2\right)^2\ +\left(y_1\ +\ y_2\right)^2\ }$$

• $$d\ =\ \sqrt{\left(x_1\ -\ x_2\right)^2\ +\left(y_1\ -\ y_2\right)^2\ }$$

Multiple Choice

Find the distance between (-4, 2) and (-1, -2).

• 5

• $$\sqrt{41}$$

• 0

Midpoint on a Number Line

If the coordinates of the endpoints of a segment are given, then the coordinate of the midpoint of the segment is half the sum of the coordinates.

Examples: Use the number line to find the coordinate of the midpoint of each segment

• Segment CE

• CE = (-4 + 2)/2 = -2/2 = -1

• Segment GA

• GA = (8 + -9)/2 = -1/2 or -0.5

Midpoint Formula in a Coordinate Plane

The midpoint of two distinct points in a coordinate plane is obtained by taking half of the sums of the corresponding x- and y-coorndinates. 

Midpoint Formula

Example 1: 

Find the midpoint of the line segment with coordinates (-3, 3) and (5, 3).  

Midpoint Formula

Example 2:

Given the coordinates (-4, 5) and (2, -3), what is the midpoint of the segment formed when the points are connected?

Midpoint Formula

Example 3:

Stella's location on the map is (1, 5) and Albert's location is (1, -1). They have decided to meet exactly halfway from each other. What are the coordinates of their meeting place?

Fill in the Blanks

Find the coordinates of the midpoint of a segment with the given endpoints.

A(0, 0), B(12, 8)

Note: Answers must be written as an ordered pair, (x, y).

Fill in the Blanks

Find the coordinates of the midpoint of a segment with the given endpoints.

K(–11, 2), L(–19, 6)

Note: Answers must be written as an ordered pair, (x, y).

Multiple Choice

Find the coordinates of the midpoint of a segment with the given endpoints.

M(11, –2), N(–9, 13)

• (-1, 5.5)

• (10, 7.5)

• (1, 5.5)