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1.1Line Segments, Distance, and Midpoint PowerPoint Presentation

1.1Line Segments, Distance, and Midpoint

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1.1Line Segments, Distance, and Midpoint

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1.1c The Midpoint Formula

1.1Line Segments, Distance, and Midpoint

CC Standard

G-GPE Use coordinates to prove simple geometric theorems algebraically [Include distance formula; relate to Pythagorean theorem]

G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; bisecting a segment; and constructing a line parallel to a given line through a point not on the line.

- The point that bisects a segment.
- Bisects?
splits into 2 equal pieces

4 4

A M B

Midpoint on a number line:

Example 1: Find the coordinate of the midpoint

x₂

x₁

The midpoint of is 2

- A segment, ray, line, or plane that intersects a segment at its midpoint.

k

A

M

B

- Used for finding the coordinates of the midpoint of a segment in a coordinate plane.
- If the endpoints are (x1,y1) & (x2,y2), then

Example 2: Find the coordinates of Q, the midpoint

of , if the endpoints of are

R(- 3, - 4) and S(5, 7)

R(x₁, y₁)

S(x₂, y₂)

Q = (1, 1.5)

Find the coordinates of the midpoint of with end points A(-2, 5) and B(6, -2)

A(x₁, y₁)

B(x₂, y₂)

Find the average of the x-values and the average of the y-values

Midpoint: (x, y) =

A

Midpoint

B

A

B

B

Ex: The midpoint of AB is M(-3,5).

One endpoint is A(4,6). Find the coordinates of B.

The total revenue of a law firm in 2000 was $680,000.

In 2010 the revenue was $980,000.

Assuming linear growth, use the midpoint formula to estimate the revenue in 2005.

A major league baseball diamond is a square having side lengths 90 feet.

i. What is the distance from home plate to second base? Overlay a rectangular coordinate

system on the baseball diamond so that the origin is at home plate, the positive x-axis

is along the first base line, and the positive y-axis is along the third base line.

ii. What are the coordinates of first, second, and third base?

iii. If the right fielder is at (305, 10), how far is the right fielder from second base?

iii. Suppose you want to position the pitching mound at equal distances from second base

and home plate. What coordinates would the pitching mound have?