[ ] [ ] EXAMPLE 4 Use scalar multiplication in a dilation

Slides:

Advertisements

Similar presentations

Dilations: (Stretching/Shrinking)  Dilations use a scale factor to reduce or enlarge shapes.  Every dilation has a center and a scale factor. Most of.

Advertisements

EXAMPLE 2 Rotating 90 Clockwise Rotate quadrilateral FGHJ 90 clockwise. SOLUTION OriginalImage (x, y) F (2, 2) G (2, 4) H (4, 4) J (5, 2) (x, –y) F ’(2,

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

SOLUTION EXAMPLE 2 Standardized Test Practice Corresponding side lengths are proportional. KL NP = LM PQ KL 12m = 10m 5m5m KL= 24 Write a proportion. Substitute.

7-2 Similarity and transformations

Geometry: Dilations. We have already discussed translations, reflections and rotations. Each of these transformations is an isometry, which means.

Transformations on the Coordinate Plane

) Math Pacing Transformations on the Coordinate Plane (3, – 2) III Q (0, 1) J (1, 4) & S (1, 0) (– 3, – 2)

EXAMPLE 1 Identify dilations Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. a. SOLUTION a. Because.

Congruence and Transformations

1. The y-axis is the perpendicular bisector of AB

Modeling Motion with Matrices Section 2-4 Before finishing this section you should be able to: Use matrices to determine the coordinates of polygons.

Chapter 9 Transformations.

An operation that moves or changes a geometric figure (a preimage) in some way to produce a new figure (an image). Congruence transformations – Changes.

) Math Pacing Transformations on the Coordinate Plane (3, – 2) III Q (0, 1) J (1, 4) & S (1, 0) (– 3, – 2)

SOLUTION EXAMPLE 1 Find the image of a glide reflection The vertices of ABC are A(3, 2), B(6, 3), and C(7, 1). Find the image of ABC after the glide reflection.

4.4 Transformations with Matrices 1.Translations and Dilations 2.Reflections and Rotations.

4-4 Geometric Transformations with Matrices Objectives: to represent translations and dilations w/ matrices : to represent reflections and rotations with.

Objective: Students will be able to represent translations, dilations, reflections and rotations with matrices.

Chapter 12.  For each example, how would I get the first image to look like the second?

1. Use a protractor to draw an angle with measure 20º.

Objective Identify and draw dilations..

EXAMPLE 2 Add and subtract matrices 5 –3 6 – –4 + a. –3 + 2

4-1 Congruence and transformations. SAT Problem of the day.

Lesson 2.7 Objective: To complete dilations on a coordinate plane.

Identify and Perform Dilations

Translations Lesson 6-1.

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Dilations MCC8.G.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

CONGRUENCE AND TRANSFORMATIONS (GET GRAPH PAPER WHEN YOU ENTER CLASS) SECTION 4.4.

Honors Geometry.  We learned how to set up a polygon / vertex matrix  We learned how to add matrices  We learned how to multiply matrices.

 An image is the new figure, and the preimage is the original figure  Transformations-move or change a figure in some way to produce an image.

EXAMPLE 3 Use matrices to rotate a figure SOLUTION STEP 1Write the polygon matrix: Trapezoid EFGH has vertices E(–3, 2), F(–3, 4), G(1, 4), and H(2, 2).

Draw a 120 rotation of ABC about P.

9.1 Translate Figure and Use Vectors Translations anslation.swf&w=894&h=762&col=%23FFFFFF&title=Geometry+Tr.

Algebra 4-2 Transformations on the Coordinate Plane

Algebra 4-2 Transformations on the Coordinate Plane

4-3 Warm Up Lesson Presentation Lesson Quiz

Warm Up A figure has vertices A, B, and C. After a transformation, the image of the figure has vertices A′, B′, and C′. Draw the pre-image and the image.

Warm up Identify the transformation ∆RST → ∆XYZ.

Algebra 4-2 Transformations on the Coordinate Plane

Objectives Identify reflections, rotations, and translations.

7-2 Similarity and transformations

Warm-Up How many lines of symmetry do the figures have? Draw them!

Transformations.

Dilations: (Stretching/Shrinking)

Dilations: (Stretching/Shrinking)

I can draw dilations in the coordinate plane.

EXAMPLE 5 Use matrix multiplication to reflect a polygon

Dilations: (Stretching/Shrinking)

Congruence and Transformations

Algebraic Representations of Dilations

4-4 Geometric Transformations with Matrices

4.1: Congruence and Transformation

EXAMPLE 2 Add and subtract matrices 5 –3 6 – –4 + a. –3 + 2

EXAMPLE 1 Translate a figure in the coordinate plane

EXAMPLE 2 Graph a reflection in y = x

9.3: Rotations.

Algebra 4-2 Transformations on the Coordinate Plane

Algebra 4-2 Transformations on the Coordinate Plane

Warm up Identify the transformation ∆RST → ∆XYZ.

Algebra 4-2 Transformations on the Coordinate Plane

4-3 Warm Up Lesson Presentation Lesson Quiz

Geometry Section 9.7.

Transformations Translation Reflection The FRAME Routine

Objective Identify and draw rotations..

Transformations on the Coordinate Plane

Presentation transcript:

[ ] [ ] EXAMPLE 4 Use scalar multiplication in a dilation The vertices of quadrilateral KLMN are K(– 6, 6), L(– 3, 6), M(0, 3), and N(– 6, 0). Use scalar multiplication to find the image of KLMN after a dilation with its center at the origin and a scale factor of . Graph KLMN and its image. 1 3 SOLUTION [ ] 1 3 – 6 – 3 0 – 6 6 6 3 0 K L M N Scale factor Polygon matrix [ ] = – 2 – 1 0 – 2 2 2 1 0 K’ L’ M’ N’ Image matrix

EXAMPLE 5 Find the image of a composition The vertices of ABC are A(– 4, 1), B(– 2, 2), and C( – 2, 1). Find the image of ABC after the given composition. Translation: (x, y) (x + 5, y + 1) Dilation: centered at the origin with a scale factor of 2 SOLUTION STEP 1 Graph the preimage ABC on the coordinate plane.

EXAMPLE 5 Find the image of a composition STEP 2 Translate ABC 5 units to the right and 1 unit up. Label it A’B’C’. STEP 3 Dilate A’B’C’ using the origin as the center and a scale factor of 2 to find A”B”C”.

GUIDED PRACTICE for Examples 4 and 5 5. The vertices of RST are R(1, 2), S(2, 1), and T(2, 2). Use scalar multiplication to find the vertices of R’S’T’ after a dilation with its center at the origin and a scale factor of 2. R’(2,4), S’(4,2), T’(4,4) ANSWER

GUIDED PRACTICE for Examples 4 and 5 6. A segment has the endpoints C( –1, 1) and D(1, 1). Find the image of CD after a 90° rotation about the origin followed by a dilation with its center at the origin and a scale factor of 2. ANSWER C’( 2, 2), D’( 2,2)