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## PowerPoint Slideshow about 'Warm Up' - lance-oconnor

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1.The y-axis is the perpendicular bisector of AB . If point A is at (–3, 5), what is the location of point B?

(3, 5)

ANSWER

ANSWER

–1

Warm-Up

2.What is the slope of the segment with endpoints at (–7, 4) and (4, –7)?

In the linen : x = 3

Point Ais 2 units left of n, so its reflectionA′is 2 units right of nat (5, 3). Also, B′ is 2 units left of nat (1, 2), and C′is 1 unit right of n at (4, 1).

Example 1

The vertices of ABC are A(1, 3),B(5, 2), and C(2, 1). Graph the reflection of ABC described.

SOLUTION

In the linem : y = 1

Point Ais 2 units above m, so A′ is 2 units below mat (1, –1). Also, B′ is 1 unit below mat (5, 0). Because point Cis on line m, you know that C = C′.

Example 1

The vertices of ABC are A(1, 3),B(5, 2), and C(2, 1). Graph the reflection of ABC described.

SOLUTION

The endpoints of FG are F(–1, 2) and G(1, 2). Reflect the segment in the line y = x. Graph the segment and its image.

The slope of y = xis 1. The segment from Fto its image, FF ′ , is perpendicular to the line of reflection y = x, so the slope of FF′ will be –1(because 1(–1) = –1). FromF, move 1.5units right and1.5units down toy = x. From that point, move1.5units right and1.5units down to locateF′(2,–1).

Example 2

SOLUTION

The slope of GG′ will also be –1. From G, move 0.5 units right and 0.5 units down to y = x. Then move 0.5 units right and 0.5 units down to locate G′(2, 1).

Example 2

Reflect FGfrom Example 2 in the line y = –x. Graph FGand its image.

(a, b) (–b, –a)

F(–1, 2)

F ′(–2, 1)

G(1, 2)

G ′(–2, –1)

Example 3

SOLUTION

Use the coordinate rule for reflecting in y = –x.

Guided Practice

4. Graph ABC with vertices A(1, 3), B(4, 4), and C(3, 1). Reflect ABC in the lines y = –x and y = x. Graph each image.

Slope of y = – xis –1.

The slope of FF′ is 1.

The product of their slopes is –1 making them perpendicular.

Guided Practice

′

5. In Example 3, verify that FF is perpendicular to y = –x.

You are going to buy books. Your friend is going to buy CDs. Where should you park to minimize the distance you both will walk?

Example 4

Reflect Bin line mto obtain B′. Then draw AB′ . Label the intersection of AB′ and mas C. Because AB′ is the shortest distance between Aand B′ and BC = B′C, park at point Cto minimize the combined distance, AC + BC, you both have to walk.

Example 4

SOLUTION

Because A′Bis the shortest distance between A′and Band AC = A′C, park at point Cto minimize the combined distance, AC + BC, you both have to walk.

Guided Practice

6. Look back at Example 4. Answer the question by using a reflection of point Ainstead of pointB.

The vertices of DEFare D(1, 2), E(3, 3), and F(4, 0). Find the reflection of DEFin the y-axis using matrix multiplication. Graph DEFand its image.

Multiply the polygon matrix by the matrix for a reflection in the y-axis.

STEP 1

D E F

–1 0

1 3 4

0 1

2 3 0

Polygon matrix

Reflection matrix

Example 5

SOLUTION

–1(1) + 0(2) –1(3) + 0(3) –1(4) + 0(0)

=

0(1) + 1(2) 0(3) + 1(3) 0(4) + 1(0)

D′ E′ F′

–1 –3 –4

=

2 3 0

Image matrix

Example 5

L′(–3, –3), M′(1, –2), and N′(–2, –1)

ANSWER

Guided Practice

The vertices ofLMN areL(–3, 3), M(1, 2),andN(–2, 1).

Find the described reflection using matrix multiplication.

7. Reflect LMNin the x-axis.

L′(3, 3), M′(–1, 2), and N′(2, 1)

ANSWER

Guided Practice

The vertices ofLMN areL(–3, 3), M(1, 2),andN(–2, 1).

Find the described reflection using matrix multiplication.

8. Reflect LMNin the y-axis.

Lesson Quiz

Graph the polygon and its reflection in the given line.

1.Quadrilateral with verticesA(–2, 1), B(1, 4), C(3, 1), D(2, –1) overy = 1.

Lesson Quiz

Graph the polygon and its reflection in the given line.

2.TriangleP(–2, 2), Q(3, 4), R(4, 1) over y = x.

A’ B’ C’

ANSWER

2 –1 0

– 2 1 0

3 4 –1

3 4 –1

Lesson Quiz

3. Use matrix multiplication to find the Image matrix when ABC is reflected in y-axis.

( , 0)

41

8

Lesson Quiz

4.Find thepointCon thex-axis soAC + BC is a minimum for A(2, 5) andB(7, 3).

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