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.

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