Find the image of the point (2,3) under each transformation.

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Find the image of the point (2,3) under each transformation. T(x-6, y-2) 2. ry-axis 3. ry = 6 4. R 0,90⁰

rx-axis(x, y) =(x,-y) ry-axis(x, y) =(-x,y) ry = x(x, y) =(y, x) 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(h, k) = (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

The vertices of triangle ABC are A (3,2), B(6,3), and C (7, 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

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

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

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

Homework is 6-5. Work on Barnyard project for remainder of class. Project due Monday. Quiz tomorrow.