Warm-up: Find the image of (2,3) under each transformation.

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Warm-up: Find the image of (2,3) under each transformation. T (x, y)=(x-6, y-2) 2. ry-axis 3.rx-axis 4. Dilate by 3 5. R180° 6. R270° 7. ry = 6 8. R 0,90⁰

Homework Answers

Let’s Talk about Notation Again Dilations: Dk(x, y) = (kx, ky) Rotations 900: R0,90°(x, y) = (-y, x) 1800: R0,180°(x, y)= (-x, -y) 2700: R0,270°(x, y)= (y, -x) Translation: T(x, y) = (x + h, y + k) Line Reflections x-axis: y-axis: y=x: rx-axis(x, y) =(x,-y) ry-axis(x, y) =(-x,y) ry = x(x, y) =(y,x)

Apply Compositions of Transformations

Vocabulary When two or more transformations are combined to form a new transformation, the result is called a composition of transformations

Example 1 The vertices of triangle ABC are A (3,2), B(6,3), and C (7, 1). Find the image of triangle ABC after the composition. Translation: (x,y)….(x-12, y) Reflection: over the x-axis

Example 2 The vertices of triangle PQR are P (2,6), Q(4,-2), and R(-3, -3). Find the image of triangle PQR after the composition. Translation: (x,y)….(x+4, y) Reflection: in the x-axis

Example 3 The endpoints of RS are R (1, -3) and S(2, -6). Graph the image of RS after the composition. Reflection: in the y-axis Rotation: 90o about the origin

Example 4 The endpoints of MN are M (-2, 1) and N(3, 4). Graph the image of MN after the composition. Reflection: in the line y=x Rotation: 180o about the origin