Presentation on theme: "FeatureLesson Geometry Lesson Main 1. Is the transformation below an isometry? Explain. No; the angles are not congruent. Lesson 9-1 Translations For Exercises."— Presentation transcript:
FeatureLesson Geometry Lesson Main 1. Is the transformation below an isometry? Explain. No; the angles are not congruent. Lesson 9-1 Translations For Exercises 2 and 3, ABCD is an image of KLMN. B and D AB and DA 2. Name the images of L and N. 3. Name the sides that correspond to KL and NK. Use the diagram below. 5. Write a rule to describe the translation MNV WZP. 4. Find the image of MNV under the translation M (–5, 4), N (–4, 6), V (–1, 5) (x, y) (x – 2, y + 5). (x, y) (x + 4, y + 3) Lesson Quiz 9-2
FeatureLesson Geometry Lesson Main Lesson 9-2 (For help, go to Lesson 3-7.) Write an equation for the line through point A that is perpendicular to the given line Reflections 3. Check Skills Youll Need 9-2
FeatureLesson Geometry Lesson Main Solutions Lesson 9-2 Reflections 1. A line perpendicular to a vertical line is a horizontal line. The equation of the horizontal line through (1, –2) is y = –2. 2. A line perpendicular to a horizontal line is a vertical line. The equation of the vertical line through (–1, –1) is x = –1. 3. The given line has slope 1. A line perpendicular to a line with slope 1 has a slope of –1. The equation of a lien with slope –1 through (–1, 2) is y = –x + 1. Check Skills Youll Need 9-2
FeatureLesson Geometry Lesson Main Lesson 9-2 Reflections 9-2 A reflection (or flip) is an isometry in which a figure and its image have opposite orientations.
FeatureLesson Geometry Lesson Main Lesson 9-2 Reflections 9-2 You can use the following two rules to reflect a figure across a line r. If a point A is on line r, then the image of A is A itself (that is, A = A). If a point B is not on line r, then r is the perpendicular bisector of.
FeatureLesson Geometry Lesson Main Lesson 9-2 Reflections 9-2 In other words, a point and its reflection image are equidistant from the line of reflection.
FeatureLesson Geometry Lesson Main If point P(2, –1), is reflected across the y-axis, what are the coordinates of its reflection image? Lesson 9-2 Reflections So the coordinates of P' are (–2, –1). Quick Check Point P is 2 units right of the reflection line, the y-axis. Therefore, the image of P' is 2 units left of the reflection line. Additional Examples 9-2 Finding a Reflection Image
FeatureLesson Geometry Lesson Main First locate vertices X, Y, and Z and draw XYZ in a coordinate plane. Locate points X, Y, and Z such that the line of reflection x = 4 is the perpendicular bisector of XX, YY, and ZZ. Draw the reflection image X Y Z. XYZ has vertices X(0, 3), Y(2, 0), and Z(4, 2). Draw XYZ and its reflection image in the line x = 4. Lesson 9-2 Reflections Quick Check Additional Examples 9-2 Drawing Reflection Images
FeatureLesson Geometry Lesson Main Show that PD and PW form congruent angles with line. PD and PW also form congruent angles with line because vertical angles are congruent. Therefore, PD and PW form congruent angles with line by the Transitive Property. Lesson 9-2 Reflections Quick Check Additional Examples Because a reflection is an isometry, PD and PD form congruent angles with line. 9-2 Real-World Connection
FeatureLesson Geometry Lesson Main Find the coordinates of the image point for each given point and reflection line. 1. R(4, –5) across x = –2 2. S(–11, 2) across y = 1 3. T(0, 5) across x-axis Lesson 9-2 Reflections XYZ has vertices X(–2, 3), Y(1, 1), and Z(2, 4). Draw XYZ and its reflection image in each line. 4.the x-axis5.the line x = 5 R'(–8, –5) S'(–11, 0) T'(0, 5) Lesson Quiz 9-2