Transformations on the Coordinate Plane. Example 2-2a A trapezoid has vertices W(–1, 4), X(4, 4), Y(4, 1) and Z(–3, 1). Trapezoid WXYZ is reflected.

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Transformations on the Coordinate Plane

Example 2-2a A trapezoid has vertices W(–1, 4), X(4, 4), Y(4, 1) and Z(–3, 1). Trapezoid WXYZ is reflected over the y -axis. Find the coordinates of the vertices of the image. To reflect the figure over the y -axis, multiply each x -coordinate by –1. (x, y)(–x, y) W(–1, 4)(1, 4) X(4, 4)(–4, 4) Y(4, 1)(–4, 1) Z(–3, 1)(3, 1) Answer:The coordinates of the vertices of the image are W(1, 4), X(–4, 4), Y(–4, 1), and Z(3, 1). Reflection

Example 2-2b A trapezoid has vertices W(–1, 4), X(4, 4), Y(4, 1), and Z(–3, 1). Graph trapezoid WXYZ and its image W X Y Z. Graph each vertex of the trapezoid WXYZ. Connect the points. Answer: Graph each vertex of the reflected image W X Y Z. Connect the points. WX YZ WX YZ Reflection

Transformations on the Coordinate Plane

Example 2-3a Triangle ABC has vertices A(–2, 1), B(2, 4), and C(1, 1). Find the coordinates of the vertices of the image if it is translated 3 units to the right and 5 units down. To translate the triangle 3 units to the right, add 3 to the x -coordinate of each vertex. To translate the triangle 5 units down, add –5 to the y -coordinate of each vertex. Answer:The coordinates of the vertices of the image are A(1, –4), B(5, –1), and C(4, –4). Translation

Example 2-3c Triangle JKL has vertices J(2, –3), K(4, 0), and L(6, –3). a. Find the coordinates of the vertices of the image if it is translated 5 units to the left and 2 units up. b. Graph triangle JKL and its image. Answer: J(–3, –1), K(–1, 2), L(1, –1) Answer: Translation

Transformations on the Coordinate Plane

Example 2-4a A trapezoid has vertices E(–1, 2), F(2, 1), G(2, –1), and H(–1, –2). Find the coordinates of the dilated trapezoid E F G H if the scale factor is 2. To dilate the figure, multiply the coordinates of each vertex by 2. Answer:The coordinates of the vertices of the image are E(–2, 4), F(4, 2), G(4, –2), and H(–2, –4). Dilation

Transformations on the Coordinate Plane

Graphing Form of a Circle Center is at (h, k) r is the radius of the circle

EX 1 Write an equation of a circle with center (3, -2) and a radius of 4.

Ex. 1: Writing a Standard Equation of a Circle Write the standard equation of the circle with a center at (-4, 0) and radius 7 (x – h) 2 + (y – k) 2 = r 2 Standard equation of a circle. [(x – (-4)] 2 + (y – 0) 2 = 7 2 Substitute values. (x + 4) 2 + (y – 0) 2 = 49 Simplify.

EX 4 Find the coordinates of the center and the measure of the radius.

Ex. 3: Graphing a circle The equation of a circle is (x+2) 2 + (y-3) 2 = 9. Graph the circle. First rewrite the equation to find the center and its radius. (x+2) 2 + (y-3) 2 = 9 [x – (-2)] 2 + (y – 3) 2 =3 2 The center is (-2, 3) and the radius is 3.