Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
1­3 Distance and Midpoints
Learning targets:
I can find distance on the number line
I can find distance in a coordinate plane
I can find the midpoint on a line
I can find the midpoint in a coordinate plane
I can find the endpoint given midpoint and endpoint
I can find measurements given expressions for segments
ο
There are 60' in 1 ο
longitude and 60' in 1 latitude. What are the coordinates, in degrees, for Orlando? Miami?
What is the length, in degrees, of each leg of the right triangle shown on the map?
Use the Pythagorean Theorem to find the distance, in degrees, between Orlando and Miami.
Dec 30­9:08 PM
Sep 2­8:05 AM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
Distance between two points: the length of the segment with those points as its endpoints.
Example 1:
1. Use the number line to find QR.
Use the number line to find each measure.
2. AC
3. CF
4. FB
Jul 26­3:05 PM
To find the distance between any two points in a coordinate plane, make a triangle and use the Pythagorean Theorem.
This gives us the distance formula.
Jul 26­3:52 PM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
Example 2:
5. Find the distance between E(­4, 1) and F(3, ­1).
Jul 26­3:39 PM
Find the distance between each pair of points.
6. E(­5, 6) and F(8, ­4)
7. J(4, 3) and K(­3, ­7)
Jul 26­4:02 PM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
Midpoint: the point halfway between the endpoints of a segment.
Example 3:
8. Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90" wide. How far is the midpoint of the couch back from the wall in feet?
Jul 26­4:06 PM
9. The temperature on a thermometer dropped from a reading of 25℉ to ­8℉. Find the midpoint of these temperatures.
Jul 26­4:13 PM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
The midpoint in a coordinate plane is found by averaging the x's and averaging the y's.
Example 4:
10. Find the coordinates of M, the midpoint of GH, for G(8, ­6) and H(­14, 12).
Jul 26­4:16 PM
Find the coordinates of the midpoint of a segment with the given coordinates.
11. A(5, 12), B(­4, 8)
12. C(­8, ­2), D(5, 1)
Jul 26­4:20 PM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
Example 5:
13. Find the coordinates of D if E(­6, 4) is the midpoint of DF and F has coordinates (­5, ­3).
Find the coordinates of the missing endpoint if P is the midpoint of EG.
14. E(­8, 6), P(­5, 10)
15. P(­1, 3), G(5, 6) Jul 26­4:25 PM
Example 6:
16. Find the measure of PR if Q is the midpoint of PR.
17. Find the measure of YZ if Y is the midpoint of XZ and XY = 2x ­ 3 and YZ = 27 ­ 4x.
18. Find the value of x if C is the midpoint of AB, AC = 4x + 5, and AB = 78.
Jul 26­4:31 PM
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Geo 1­3 Lesson with notes 1st a.notebook
September 08, 2015
Segment bisector: any segment, line, or plane that intersects a segment at its midpoint.
M is the midpoint of PQ. Plane A, MJ, KM, and point M are all bisectors of PQ. They bisect PQ.
Jul 26­4:38 PM
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