Geometry 1-6

Midpoint and Distance in the Coordinate Plane

Students will be able to…

Develop and apply the formula for midpoint.

Use the distance formula to find the distance between two points.

Learning Targets

Find the area and the perimeter of…

1. A rectangle with width 4 and length 72. A triangle with base 8 and height 10

Find the area and circumference of…3. A circle with radius 4

Warm-up

Write the coordinates of the points plotted on

the graphA. ___________ B. _____________ C. _____________ D. ______________

Warm-up Day 2

Homework Check

Homework Check

Homework Check

Homework Check

Coordinate plane:

a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis).

Review of Vocabulary

Review of Coordinate Planes

1. Label the graph’s x-axis and y-axis.  2. Review plotting coordinates in the form (x,y). 3. Plot points and label by the appropriate letter.H. (2,7) I. (-5, -5) J. (-3, 6) K. (1, -4)  4. Write the coordinates of the points plotted on the graph A. ____________ B. _____________C. _____________ D. ______________

Review of Coordinate Planes

1. Label the graph’s x-axis and y-axis.  2. Plot points and label by the appropriate letter. H. (4,-2) I. (-5, 0)

J. (-3,6) K. (-1, -1) 3. Write the coordinates of the points plotted on the graph

A. ___________ B. _____________

C. ____________ D. _____________

Midpoint Formula: the midpoint M of with endpoints A and B.  

Formula:

Midpoint Formula

A B

( 𝑥1+𝑥22,𝑦1+𝑦22 )

1. Find the coordinates of the midpoint of with

endpoints E(-2, 3) and F(5, -3).

Finding the Coordinates of a Midpoint

2. Find the coordinates of the midpoint of with

endpoints C(-2, -1) and D(4, 2).

Finding the Coordinates of a Midpoint

3. Find the coordinates of the midpoint of with

endpoints Y(-4, 6) and Z(3, 8).

Finding the Coordinates of a Midpoint

Finding the coordinates of one endpointSteps: 1. Let the coordinates of the missing endpoint equal (x, y) 2. Use the Midpoint Formula 3. Find the x coordinate 4. Find the y coordinate 5. Rewrite the coordinates

Finding the Coordinates of an Endpoint

1. M is the midpoint of A has coordinates (2, 2) and M has coordinates (4, -3). Find the coordinates of B.

Finding the Coordinates of an Endpoint

2. S is the midpoint of R has coordinates (-6, -1) and S has coordinates (-1, 1). Find the coordinates of T.

Finding the Coordinates of an Endpoint

3. B is the midpoint of A has coordinates (-6, -2) and B has coordinates (9, 3). Find the coordinates of C.

Finding the Coordinates of an Endpoint

4. Y is the midpoint of B has coordinates (-4, -4) and Y has coordinates (-2, 3). Find the coordinates of A.

Finding the Coordinates of an Endpoint

What is a square root? What does it mean?

You are looking for a number times itself that will give you the value under the square root.

How can we calculate it using a calculator?

Type 2nd button and then square root Let’s find it on everyone’s calculator. Then type the number you are looking for the square root of.

Review of Square Roots

What is

What is

Why is rounding important?

Review of Square Roots

Distance Formula:

In a coordinate plane, the distance d between two points and is

Distance Formula

1. Find XY using the distance formula.

X(-2, 4) and Y(6, 1).

Distance Formula

2. Find EF using the distance formula.

E(-2, 1) and F(-5, 5).

Distance Formula

3. Find XY using the distance formula.

X(5, 10) and Y(-5, -10).

Distance Formula

What is the midpoint formula?

What is the distance formula?

Review