### Geometry Home Practice: Translation and Reflection**Name:** ___________________________________ **Block:** ____________________________________#### Use the translation (x, y) → (x + 6, y - 3).1. What is the image of A(3, 2)? 2. What is the image of B(-4, 1)? 3. What is the preimage of C'(2, -7)? 4. What is the preimage of D'(-3, -2)? ---#### The vertices of ∆ABC are A(-1, 1), B(4, -1), and C(2, 4). Graph the image of the triangle using prime notation.**5. (x, y) → (x - 3, y + 5)** (A graph is shown on a coordinate plane with the transformation (x-3, y+5) applied to triangle ABC.)**6. (x, y) → (x - 4, y - 2)** (A graph is shown on a coordinate plane with the transformation (x-4, y-2) applied to triangle ABC.)---#### ΔA′B′C′ is the image of ΔABC after a translation. Write a rule for the translation. Then verify that the translation is an isometry.**7.** (Graph of preimage ∆ABC and image ∆A'B'C' on a coordinate plane.)#### Name the vector and write its component form.**9.** (Graph of a vector JM on a coordinate plane.)**10.** (Graph of a vector XY on a coordinate plane.)---#### Find the value of each variable in the translation.(Diagram showing geometric shapes with angles and linear measurements labeled. Angles are given as 100°, a°, 5d0°, 80°, 31°. Linear measurements are given as 13, 2b, 8, 12, 20, 3c + 2, b = 5.)**Diagram Explanation:**- One irregular quadrilateral: - Angles: 100°, a°. - Sides: 13, 2b. - Another irregular quadrilateral: - Angles: 5d0°, 80°. - Sides: 8, b = 5 as given for missing side. - Right-angled triangle: ### Graph the reflection of the polygon in the given line#### 1. x-axisThis graph demonstrates the reflection of a polygon across the x-axis. The polygon's original and reflected images are shown on a standard Cartesian coordinate grid.#### 2. y-axisThis graph demonstrates the reflection of a polygon across the y-axis. The original and reflected images of the polygon are plotted on a Cartesian grid.#### 3. x = -1In this graph, the polygon is reflected across the vertical line $x = -1$. The coordinate system clearly shows the transformation involved.#### 4. y = 1This graph shows the polygon's reflection across the horizontal line $y = 1$. The original and reflected polygons are illustrated on the coordinate grid.#### 5. y = -xThis graph reflects the polygon across the line $y = -x$. The coordinate transformation is shown with the initial and reflected images on the grid.#### 6. y = xIn this example, the polygon is reflected across the line $y = x$, with the transformation displayed on a standard Cartesian plane.### Multiple ReflectionsThe vertices of $ \Delta ABC $ are $ A(-2, 1) $, $ B(3, 4) $, and $ C(3, 1) $. 1. **Reflect $ \Delta ABC $ in the line $ y = 1 $.**2. **Reflect $ \Delta A'B'C' $ in the line $ y = -2 $.**3. **Graph $ \Delta A''B''C'' $.** Each of these reflections is shown on separate graphs:#### 7. Reflection in $ y = 1 $, then in $ y = -2 $This graph demonstrates the cumulative reflection process, first in the line $ y = 1 $ followed by $ y = -2 $.#### 8. Reflection in $ x = 4 $, then in $ y = -1 $Here, the polygon is first reflected in the line $ x = 4 $ and then in $ y = -1 $. The combined transformations are depicted on the grid.#### 9. Reflection in $ y = x $, then in $ x = -2 $This graph reflects the polygon first in the line $ y = x $ and then in

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Answered: Use the translation (x, y) (x + 6, y -…

Use the translation (x, y) (x + 6, y - 3). | 1. What is the image of A(3, 2)? 2. What is the image of B(-4, 1)? 3. What is the preimage of C'(2, -7)? 4. What is the preimage of D'(-3,–2)? | |

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 58E

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