**Reflection of Quadrilaterals Over the X-Axis****Problem:**Quadrilateral $ABCD$ has vertices $A = (0, 4)$, $B = (0, 3)$, $C = (3, 0)$, and $D = (3, 4)$. Quadrilateral $A'B'C'D'$ is formed when quadrilateral $ABCD$ is reflected over the x-axis. What are the coordinates of quadrilateral $A'B'C'D'$?**Options:**Select one:- $\bigcirc$$ A' = (0, -4), B' = (0, -3), C' = (3, 0), D' = (3, -4) $- $\bigcirc$$ A' = (-4, 0), B' = (-3, 0), C' = (0, 3), D' = (4, 3) $- $\bigcirc$$ A' = (0, -4), B' = (0, -3), C' = (-3, 0), D' = (-3, -4) $- $\bigcirc$$ A' = (0, 4), B' = (0, 3), C' = (-3, 0), D' = (-3, 4) $**Explanation:**When a point $ (x, y) $ is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign.Let's apply this to each vertex:- For $ A = (0, 4) $, the reflection is $ A' = (0, -4) $.- For $ B = (0, 3) $, the reflection is $ B' = (0, -3) $.- For $ C = (3, 0) $, the reflection is $ C' = (3, 0) $ (no change since y is 0).- For $ D = (3, 4) $, the reflection is $ D' = (3, -4) $.Therefore, the correct coordinates for $ A'B'C'D' $ after reflecting $ABCD$ over the x-axis are:\( A' = (0, -

The reflection rule for reflection over x axis says that (x,y) will become (x,-y).

Quadrilateral ABCD has vertices A = (0, 4), B = (0, 3), C = (3, 0), and D= (3 ,4). Quadrilateral A'B'C'D' is formed when quadrilateral ABCD is reflected over the x-axis. What are the coordinates of quadrilateral A'B'C'D'? Select one: O A'= (0, -4), B' = (0, -3), C = (3, 0), and D' = (3, -4) O A' = (-4, 0), B = (-3, 0), C = (0, 3), and D' = (4, 3) %3D O A' = (0, -4), B' = (0, -3), C = (-3, 0), and D' = (-3, -4) %3D O A'= (0, 4), B' = (0, 3), C = (-3, 0), and D = (-3, 4)

Quadrilateral ABCD has vertices A = (0, 4), B = (0, 3), C = (3, 0), and D= (3 ,4). Quadrilateral A'B'C'D' is formed when quadrilateral ABCD is reflected over the x-axis. What are the coordinates of quadrilateral A'B'C'D'? Select one: O A'= (0, -4), B' = (0, -3), C = (3, 0), and D' = (3, -4) O A' = (-4, 0), B = (-3, 0), C = (0, 3), and D' = (4, 3) %3D O A' = (0, -4), B' = (0, -3), C = (-3, 0), and D' = (-3, -4) %3D O A'= (0, 4), B' = (0, 3), C = (-3, 0), and D = (-3, 4)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Concept explainers

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.

Question

**Reflection of Quadrilaterals Over the X-Axis**

**Problem:**
Quadrilateral $ABCD$ has vertices $A = (0, 4)$, $B = (0, 3)$, $C = (3, 0)$, and $D = (3, 4)$. Quadrilateral $A'B'C'D'$ is formed when quadrilateral $ABCD$ is reflected over the x-axis. What are the coordinates of quadrilateral $A'B'C'D'$?

**Options:**
Select one:
- $\bigcirc$$ A' = (0, -4), B' = (0, -3), C' = (3, 0), D' = (3, -4) $
- $\bigcirc$$ A' = (-4, 0), B' = (-3, 0), C' = (0, 3), D' = (4, 3) $
- $\bigcirc$$ A' = (0, -4), B' = (0, -3), C' = (-3, 0), D' = (-3, -4) $
- $\bigcirc$$ A' = (0, 4), B' = (0, 3), C' = (-3, 0), D' = (-3, 4) $

**Explanation:**

When a point $ (x, y) $ is reflected over the x-axis, the x-coordinate remains the same, but the y-coordinate changes sign.

Let's apply this to each vertex:
- For $ A = (0, 4) $, the reflection is $ A' = (0, -4) $.
- For $ B = (0, 3) $, the reflection is $ B' = (0, -3) $.
- For $ C = (3, 0) $, the reflection is $ C' = (3, 0) $ (no change since y is 0).
- For $ D = (3, 4) $, the reflection is $ D' = (3, -4) $.

Therefore, the correct coordinates for $ A'B'C'D' $ after reflecting $ABCD$ over the x-axis are:
\( A' = (0, -

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