Quiz 9-1 Translations And Reflections Answers

Understanding transformations like translations and reflectionsis fundamental in geometry, forming the bedrock for more complex topics like congruence and similarity. This article provides the answers and detailed explanations for Quiz 9-1 on these core concepts, empowering you to master them confidently.

Introduction Quiz 9-1 focuses on the core geometric transformations: translations and reflections. A translation slides every point of a figure a fixed distance in a specific direction, preserving its size, shape, and orientation. A reflection flips a figure over a line of reflection, also preserving size and shape but changing orientation. Correctly identifying the type of transformation and finding the image coordinates requires a clear understanding of the rules governing each. This guide offers the solutions and step-by-step reasoning for each problem on the quiz.

Solutions and Explanations

1. Problem: Given point A(3, -2), perform a translation 5 units right and 3 units down. Find A'. Answer: A'(8, -5) Explanation: Moving 5 units right increases the x-coordinate by 5 (3 + 5 = 8). Moving 3 units down decreases the y-coordinate by 3 (-2 - 3 = -5). Apply the same change to every point.

2. Problem: Given triangle ABC with vertices A(1, 2), B(4, 2), C(2, 5). Reflect it over the x-axis. Find the coordinates of A', B', and C'. Answer: A'(1, -2), B'(4, -2), C'(2, -5) Explanation: Reflecting over the x-axis changes the sign of the y-coordinate while keeping the x-coordinate the same. Apply this to each vertex.

3. Problem: Given point P(-4, 3). Translate it 2 units left and 1 unit up. Find P'. Answer: P'(-6, 4) Explanation: Moving 2 units left decreases the x-coordinate by 2 (-4 - 2 = -6). Moving 1 unit up increases the y-coordinate by 1 (3 + 1 = 4).

4. Problem: Given quadrilateral DEFG with vertices D(0, 1), E(2, 1), F(3, 3), G(1, 3). Reflect it over the line y = 1. Find the coordinates of D', E', F', and G'. Answer: D'(0, 1), E'(2, 1), F'(3, 1), G'(1, 1) Explanation: Reflecting over the horizontal line y = 1 means the line of reflection is the same height as the original points. The x-coordinate remains unchanged. The y-coordinate changes so that the point is equidistant below the line. For D(0,1): distance to line is 0, so D' is also at y=1. For E(2,1): distance 0, E' at y=1. For F(3,3): distance to y=1 is 2 units up, so F' is 2 units down at y=1 (3 - 2 = 1). Similarly, G(1,3) becomes G'(1,1).

5. Problem: Given point H(5, -1). Perform a translation 3 units left and 4 units up. Find H'. Answer: H'(2, 3) Explanation: Moving 3 units left decreases x by 3 (5 - 3 = 2). Moving 4 units up increases y by 4 (-1 + 4 = 3).

6. Problem: Given triangle XYZ with vertices X(2, 4), Y(6, 4), Z(4, 7). Reflect it over the line x = 2. Find the coordinates of X', Y', and Z'. Answer: X'(2, 4), Y'(2, 4), Z'(2, 7) Explanation: Reflecting over the vertical line x = 2 means the line of reflection is the same x-value as the original points. The y-coordinate remains unchanged. The x-coordinate changes so that the point is equidistant left or right of the line. For X(2,4): on the line, X' is (2,4). For Y(6,4): distance to x=2 is 4 units right, so Y' is 4 units left at x=2 (6 - 4 = 2), y=4. For Z(4,7): distance to x=2 is 2 units right, so Z' is 2 units left at x=2 (4 - 2 = 2), y=7.

7. Problem: Given point I(-3, 0). Translate it 1 unit right and 5 units down. Find I'. Answer: I'(-2, -5) Explanation: Moving 1 unit right increases x by 1 (-3 + 1 = -2). Moving 5 units down decreases y by 5 (0 - 5 = -5).

8. Problem: Given pentagon JKLMN with vertices J(1, 2), K(3, 2), L(4, 4), M(3, 6), N(1, 4). Reflect it over the line y = 3. Find the coordinates of J', K', L', M', and N'. Answer: J'(1, 4), K'(3, 4), L'(4, 2), M'(3, 0), N'(1, 2) Explanation: Reflecting over y = 3 (horizontal line). The line is at y=3. The x-coordinate stays the same. The y-coordinate changes so the point is equidistant below the line. For J(1,2): distance to y=3 is 1 unit down, so J' is 1 unit up at y=4 (2 + 2 = 4? Wait, distance down is 1, so reflection is 1 unit above the line? Correct: distance below is 1, so reflection is 1 unit above the line, y=3+1=4). For K(3,