1.3: Distance and Midpoints

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1.3 Use Midpoint and Distance Formulas

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Presentation transcript:

1.3: Distance and Midpoints Objective: I will be able to… -Calculate the distance between 2 points -Calculate the midpoint of 2 points

You graphed points on the coordinate plane. Find the distance between two points. Find the midpoint of a segment. Then/Now

NEW VOCAB! Distance: the length of the segment between 2 points Irrational number: a number that cannot be expressed as a terminating or repeating decimal Midpoint: the point that is halfway between the endpoints of a line segment Segment Bisector: any segment, line, or plane that intersects a segment at its midpoint

Real world examples -Get into groups -Complete front and back of worksheet together -I want to see some serious explanations! No one word answers or “I don’t know”!

Let’s discover the distance formula! First, we’ll plot two points: (0,0) and (3,4) We want to calculate the shortest distance between these two points. We will create a right triangle. How do we find the lengths of our legs? What side is the “distance” on?

Concept

Find the distance between E(–4, 1) and F(3, –1). Find Distance on a Coordinate Plane Find the distance between E(–4, 1) and F(3, –1). Example 2

Find the distance between A(–3, 4) and M(1, 2). Example 2

Concept

DRAG RACING The length of a drag racing strip is. mile long DRAG RACING The length of a drag racing strip is mile long. How many feet from the finish line is the midpoint of the racing strip? (Remember: 1 mile = 5,280 feet) A. 330 ft B. 660 ft C. 990 ft D. 1320 ft Example 3

Let’s discover the midpoint formula! Graph 2 points J (1,2) and E (-3,5) We will draw a line segment between them Thinking back to how we find a midpoint on a number line, how do you think we find a midpoint on a coordinate plane?

Concept

A. (–10, –6) B. (–5, –3) C. (6, 12) D. (–6, –12) Example 4

Find the Coordinates of an Endpoint Example 5

Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5). B. (–10, 13) C. (15, –1) D. (17, –11) Example 5

A. 1 B. 10 C. 5 D. 3 Example 6

Segment Bisector: any segment, line, or plane that intersects a segment at its midpoint Q A B P

E A B C D

Homework Assignment pg. 31 #22-24, 31-32, 47-49, 68