holt mcdougal geometry 1-6 midpoint and distance in the coordinate plane 1-6 midpoint and distance...
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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
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
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
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
coordinate planeleghypotenuse
Vocabulary
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).
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.
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Mem
orize
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)
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).
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:
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).
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:
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).
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.
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Memorize!
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)
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
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.
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)
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
1.6 Day 2
Pythagorean Theorem
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate PlanePYTHAGOREAN THEOREM
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
What is the height of the wall?
Holt McDougal Geometry
1-6 Midpoint and Distance in the Coordinate Plane
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.
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.
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
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