holt mcdougal geometry 1-6 midpoint and distance in the coordinate plane 1-6 midpoint and distance...
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![Page 1: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/1.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane1-6 Midpoint and Distance
in the Coordinate Plane
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
![Page 2: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/2.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Warm Up
1. Graph A (–2, 3) and B (1, 0).
2. Find CD. 8
3. Find the coordinate of the midpoint of CD. –2
4. Simplify.
4
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Develop and apply the formula for midpoint.
Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.
Objectives
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
coordinate planeleghypotenuse
Vocabulary
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
A coordinate plane is a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y).
![Page 6: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/6.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
You can find the midpoint of a segment by using the coordinates of its endpoints. Calculate the average of the x-coordinates and the average of the y-coordinates of the endpoints.
![Page 7: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/7.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Mem
orize
![Page 8: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/8.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Example 1: Finding the Coordinates of a Midpoint
Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).
= (–5, 5)
![Page 9: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/9.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Try One!! You can do it!
Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Example 2: You know the midpoint, now find the endpoint!
M is the midpoint of XY. X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.
Step 1 Let the coordinates of Y equal (x, y).
Step 2 Use the Midpoint Formula:
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
12 = 2 + x Simplify.
– 2 –2
10 = x
Subtract.
Simplify.
2 = 7 + y– 7 –7
–5 = y
The coordinates of Y are (10, –5).
![Page 12: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/12.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Try one!!
S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T.
Step 1 Let the coordinates of T equal (x, y).
Step 2 Use the Midpoint Formula:
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Check It Out! Example 2 Continued
Step 3 Find the x-coordinate.
Set the coordinates equal.
Multiply both sides by 2.
–2 = –6 + x Simplify.
+ 6 +6
4 = x
Add.
Simplify.
2 = –1 + y+ 1 + 1
3 = y
The coordinates of T are (4, 3).
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Mix and Match
When the music stops find a partner.Find the midpoint between your point and your partner’s point.Double check your answer with your partner.
![Page 15: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/15.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Memorize!
![Page 16: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/16.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Example 3: Using the Distance Formula
Find the length of segment FG if:
F(1, 2), G(5, 5)
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Try one!
Find the length of segment AB if:
A(-9, 2) B(3,-5)
≈13.9
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Distance FormulaLine Up
Find the distance between your two points and line up from least to greatest by answer.
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Warm Up
Find the distance and midpoint between the two points.
1.) (-2, 6) and (8, 0)
2.) (1, -7) and (9, 3)
![Page 20: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/20.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
1.6 Day 2
Pythagorean Theorem
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate PlanePYTHAGOREAN THEOREM
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
![Page 23: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/23.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
![Page 24: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/24.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
What is the height of the wall?
![Page 25: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/25.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
![Page 26: Holt McDougal Geometry 1-6 Midpoint and Distance in the Coordinate Plane 1-6 Midpoint and Distance in the Coordinate Plane Holt Geometry Warm Up Warm Up](https://reader036.vdocuments.net/reader036/viewer/2022081721/56649e405503460f94b3221f/html5/thumbnails/26.jpg)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Lesson Quiz: Part I
(17, 13)
(3, 3)
12.73. Find the distance, to the nearest tenth, between
S(6, 5) and T(–3, –4).
4. The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1), and C(–4, –2). Find the perimeter of ∆ABC, to the nearest tenth. 26.5
1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).
2. K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L.
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Lesson Quiz: Part II
5. Find the lengths of AB and CD and determine whether they are congruent.
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Warm Up
Use the Pythagorean Theorem to find the missing side length.
1.) a = 3, b = 4
2.) a = 5, c = 13
3.) b = 10, c = 15
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Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Warm Up
1.) Find the distance and midpoint, to the nearest tenth, between the points S(6, 5) and T(-3, -4)
Use the Pythagorean theorem to find the missing side length.
2.) a = 7, b = 12
3.) b = 4, c = 5