Alternative transcript:

the x-coordinate. Reflection in x-axis: (x, y) : (x,y) →→ (x₁ - y) Reflection in y-axis: (x, y) →→ (-x, y) In a reflection, the original figure and its image are identical. Algebra: Reflection BAJU 2.3-Rotations ☆ A rotation, or turn, is a transformation in which a figure is rotated about a point called the center of rotation. The number of degrees figure rotates is the angle of rotation. Turn CCW: Rotations in the Coordinate Plane * When a point (x, y) is rotated counter clockwise about the origin, the following are true: •For a rotation of 90°: (x,y) → (-y, x) For a rotation of 180°: (x, y) → (x,-v) · For a rotation of 270°: (x, y) →→→ (y₁ - x) (-y) .(x, y) ☆ In a rotation. original figure and Angle of Robation its image are Tidentical. CW: center of Rotation (x₂-x) ☆ When a point (x,x) is rotated clockwise about the origin, the following are true: •For a rotation of 90°: (x, y) →→→ (x,-x) Same as 270° CCW. - For a rotation of 270°: (x,y) →→→ (-y, x) Same as 90 CCW 2.4-Congruent Figures & A rigid motion is a transformation that preserves legth and angle measure. Translations, reflections, and rotations are rigid motions. Congruent Figures # Two figures are congruent figures when one can be obtained from the. other by a sequence of rigid motions. Congruent figures have the same size and the same shape. Angles with the Same measure are called congruent. congruent angles. Sides with the same measure are called congruent sides. 10-31 The triangles below are congruent. B 40 Sides: AB=DE, BC= EF, AC = DF Angles: <A = 2D, <B=LE₁/C#/F 20X72 2.5-Dilations as a plant figure ★ A dilation is a transformation in which a is made larger or smaller with respect to a point called the center of dilation. In a dilation. the angles of the image and the original figure are congruent. center of dilation Dilations in the Coordinate Plane ☆ Words: To dilate a figure with respect to the origin. mutiply the coordinates of each vertex by the scale factor K. Algebra (x,y) →→→→Kx, Ky) • When K²), the dilation is an enlargemet. •When K>0 and k≤1, the dilation is a reduction. lengths of the In a dilation, the value of the ratio of the side image to the corresponding side lengths. of the original figure is the scale factor of the dilation. 2.6-Similar Figures * Dilations do not preserve length, so dilations is a dilation or a sequence of dilations and rigid. are not rigid motions. A similarity transformation motions. Similar Figures ☆ ☆ Two figures are similar figures when one can be obtained from the other by a similarity transformation. Similar figures have the same shape but not recessarily the same size. The triangles below. are similar corresponding argles of similar figures are congruent Corresponding side lengths of similar figures are proportional Side Lengths: A² = 2 = OF AB BC AC EF DF DE Angles: <A=2D, <B=2E₁ < C = <F & 2.7- Perimeters and Areas of Siristor Figures Perimeters of Similar figures. When two figures are similar, the value of the ratio of their perimeters is equal to the value of the ratio of their corresponding side lenghs. Perimeter of AABC - AB_BC_AC Perimeter of A DEF DE EF DE Areas of Similar Figures * When two figures are similar, the value of the ratio of their areas is equal to the square of the value of the ratio of their corresponding side lengths. Area DF AABC = (AB) = (BC) = (AC) nf of A DEF DE