APRIL 30 TH, 2014 Midpoint & Distance. Get notes out! Write this down Vocabulary Midpoint: divides a segment into two congruent pieces Segment Bisector:

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Presentation transcript:

APRIL 30 TH, 2014 Midpoint & Distance

Get notes out! Write this down Vocabulary Midpoint: divides a segment into two congruent pieces Segment Bisector: a point, line, plane, or ray that divides a segment at its midpoint

Use the Picture What is the midpoint of AC? What bisects segment BE? If AD = 15, how long is CD? Is DB = 15? How can you show congruent segments in a diagram?

Points on a Coordinate Plane What is a point? How do you show a point’s location on the coordinate plane? What comes first? A(x 1, y 1 )B(x 2, y 2 )

Midpoint Formulas Number Line: Coordinate Plane:

Try One! Calculate the midpoint of segment EB.

NC Final Exam Question If Jennifer and Jane are best friends. They placed a map of their town on a coordinate grid and found the point at which each of their house lies. If Jennifer’s house lies at (9, 7) and Jane’s house is at (15, 9) and they wanted to meet in the middle, what are the coordinates of the place they should meet?

NC Final Exam Examples If you are given the midpoint of a segment and one endpoint. Find the other endpoint. a. midpoint: (6, 2) endpoint: (1, 3) b. midpoint: (-1, -2) endpoint: (3.5, -7)

Distance Formula Number Line: Coordinate Plane:

You Try It! Calculate the distance between D and A.

Partner Race The first group to get all of the answers correct gets CANDY!

Distance & Ratios Point P divides in the ratio 3 to What does this mean? 2. Give some examples for the lengths of AP, PB, and AB!

Example Find the coordinate of point P that lies along the directed line segment from A(3, 4) to B(6, 10) and partitions the segment in the ratio of 3 to 2.

Example Find the coordinates of the point P that lies along the directed segment from A(1, 1) to B(7, 3) and partitions the segment in the ratio of 1 to 4

Distance Find the coordinates of point P that lies along the directed line segment from M to N and partitions the segment in the ratio of 3 to 2

NC Final Exam Question Example

Line Up Calculate the distance of the ordered pairs on your sheet. Line up in ascending order of distances

Homework Worksheet Make sure you show your work or no credit!!!