Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane 1-7 Transformations in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

1-7 Transformations in the Coordinate Plane transformation reflection preimage rotation image translation Vocabulary

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane A transformation is a change in the position, size, or shape of a figure. The original figure is called the preimage. The resulting figure is called the image. A transformation maps the preimage to the image. Arrow notation () is used to describe a transformation, and primes (’) are used to label the image.

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane What’s different between the Preimage and the Image?

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane To find coordinates for the image of a figure in a translation, add a to the x-coordinates of the preimage and add b to the y-coordinates of the preimage. Translations can also be described by a rule such as (x, y)  (x + a, y + b).

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Find the coordinates for the image of ∆ABC after the translation (x, y)  (x + 2, y - 1). Draw the image. Example 3: Translations in the Coordinate Plane Step 1 Find the coordinates of ∆ABC. The vertices of ∆ABC are A(–4, 2), B(–3, 4), C(–1, 1).

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Example 3 Continued Step 2 Apply the rule to find the vertices of the image. A’(–4 + 2, 2 – 1) = A’( – 2, 1) B’(–3 + 2, 4 – 1) = B’( – 1, 3) C’(–1 + 2, 1 – 1) = C’(1, 0) Step 3 Plot the points. Then finish drawing the image by using a straightedge to connect the vertices.

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Example 1A: Identifying Transformation Identify the transformation. Then use arrow notation to describe the transformation. The transformation cannot be a reflection because each point and its image are not the same distance from a line of reflection. 90° rotation, ∆ABC  ∆A’B’C’

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Example 1B: Identifying Transformation Identify the transformation. Then use arrow notation to describe the transformation. The transformation cannot be a translation because each point and its image are not in the same relative position. reflection, DEFG  D’E’F’G’

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Check It Out! Example 1 Identify each transformation. Then use arrow notation to describe the transformation. translation; MNOP  M’N’O’P’rotation; ∆XYZ  ∆X’Y’Z’ a.b.

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Check It Out! Example 3 Find the coordinates for the image of JKLM after the translation (x, y)  (x – 2, y + 4). Draw the image. Step 1 Find the coordinates of JKLM. The vertices of JKLM are J(1, 1), K(3, 1), L(3, –4), M(1, –4),.

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Check It Out! Example 3 Continued Step 2 Apply the rule to find the vertices of the image. J’(1 – 2, 1 + 4) = J’(–1, 5) K’(3 – 2, 1 + 4) = K’(1, 5) L’(3 – 2, –4 + 4) = L’(1, 0) M’(1 – 2, –4 + 4) = M’(–1, 0) Step 3 Plot the points. Then finish drawing the image by using a straightedge to connect the vertices. J’J’ K’K’ M’M’ L’L’

Holt McDougal Geometry 1-7 Transformations in the Coordinate Plane Directions for Today: 1)Work on Activity 2, “Exploring Rotations”, on the Chrome Books 2)When finished, put your Chrome Book away and you may begin working on your page of notes for our test. 1)Here is what I would have ready to go for the test 2)Homework, Notes, etc. in order of the sections 1)Definitions or terms 1)You will not need to know these by heart but it is good to know 2)EQUATIONS 1)Distance Formula 2)Midpoint Formula 3)Pythagorean Theorem 4)Area and Circumference of a Circle 5)Area/Perimeter of Square or Rectangle 6)Area/Perimeter of Triangle 7)Supplementary and Complementary Angles 3)LOOK/REVIEW AT YOUR FIRST QUIZ!!!!!!