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The location of a point P can be identified by polar coordinates of the form (r, θ), where r is the directed distance from the pole, or origin, to point P and θ is the measure of the directed angle formed by the ray from the pole to point P and the polar axis Example: Graph each point radians in standard position

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9-1 Study Guide and Intervention Polar Coordinates Graph Polar Coordinates A polar coordinate system uses distances and angles to record the position of a 

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2 fév 2015 · Study Guide, Practice, and Enrichment masters TeacherWorksTM polar coordinates in the form (r, ), where r is the distance from the pole, or 

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coordinate plane Each point of the image and its corresponding point on the preimage must be the same distance from the line of reflection • To reflect 

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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 9-1

Chapter 9 5 Glencoe GeometryDraw Reflections A reflection is a flip of a figure in a line called the line of

reflection. Each point of the preimage and its corresponding point on the image are the same distance from the line. A reflection maps a point to its image. If the point is on the line of reflection, then the image and preimage are the same point. If t he point does not lie on the line of reflection, the line of reflection is the perpendicular b isector of the segment joining the two points. Construct the image of quadrilateral ABCD under a reflection in line m . Draw a perpendicular from each vertex of the quadrilateral to m . Find vertices A , B", C", and D" that are the same distance from m on the other side of m. The image is A" B" C" D .Exercises Use the figure and given line of reflection. Then draw the reflected ima ge in this line using a ruler. 1. m H' J' K' HJK 2. t P' N' M' LMN O P 3. p R' T' S' QR S T U 4. r " 5. 6.

9-1Study Guide and Intervention

Reflections

Examplem

CAD B A B' C' D' a Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 9 6 Glencoe Geometry

Study Guide and Intervention (continued)9-1

Draw Reflections In The Coordinate Plane Reflections can be performed in the coordinate plane. Each point of the image and its corresponding point on the preimage must be the same distance from the line of reflection.

• To reflect a point in the

x -axis, multiply its y -coordinate by 1.

• To reflect a point in the

y -axis, multiply its x -coordinate by 1.

• To reflect a point in the line

y = x, interchange the x-and y-coordinates. Quadrilateral DEFG has vertices D(-2, 3), E(4, 4), F(3, -2), and G(-3, -1). Find the image under reflection in the x-axis.

To find an image for a reflection in the

x -axis, use the same x -coordinate and multiply the y -coordinate by

1. In symbols,

a , b) → (a, -b). The new coordinates are D"(-2, -3), E"(4, -4), F (3, 2), and G

3, 1). The image is

D " E" F" G".

Exercises

Graph ?FGH and its image in the given line.

1. x = -1 2. y = 1

Graph quadrilateral

ABCD and its image in the given line.

3. y = 0 4. x = 1

Graph each figure and its image under the given reflection.

5. ?DEF with D(-2, -1), E(-1, 3), 6. ABCD with A(1, 4), B(3, 2), C(2, -2),

F (3, -1) in the x-axis D(-3, 1) in the y-axis xy O D" E" F" G" DE F G y x y x xy O F" D" E" FDE xy O D" C" B" A" D CB A

Example

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