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Which of the given shapes has a larger area? y A D C S the rectangle the triangle

Which of the given shapes has a larger area? y A D C S the rectangle the triangle

Algebra and Trigonometry (6th Edition)
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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**Question:** Which of the given shapes has a larger area? [Graph Description] - The graph features a coordinate plane with axes labeled \( x \) and \( y \). - The graph spans both positive and negative directions of the \( x \) and \( y \) axes, covering 12 units on the \( x \)-axis and 12 units on the \( y \)-axis. - There are two geometric shapes plotted on the graph: a rectangle \( ABCD \) and a triangle \( QRS \). **Rectangle \( ABCD \):** - Vertex \( A\) is at (0, 2) - Vertex \( B\) is at (4, 2) - Vertex \( C\) is at (4, -2) - Vertex \( D\) is at (0, -2) **Triangle \( QRS \):** - Vertex \( Q\) is at (0, -4) - Vertex \( R\) is at (6, 4) - Vertex \( S\) is at (8, -4) **Options:** - The rectangle - The triangle **Buttons:** - Back - Next **Instructions:** Analyze the shapes \( ABCD \) and \( QRS \) on the graph and determine which shape has a larger area. Select the appropriate option from "the rectangle" or "the triangle" and click the "Next" button to proceed once you have made your selection. **Explanation of Diagram:** - The coordinate plane is divided into a grid with each small square representing one square unit. - The rectangle \( ABCD \) is plotted in the first and fourth quadrants. - The triangle \( QRS \) is plotted in the fourth quadrant and extends into the first quadrant. To determine the areas: 1. **Rectangle \( ABCD\):** - Length: \( |4 - 0| = 4 \) units - Width: \( |2 - (-2)| = 4 \) units - Area: \( 4 \times 4 = 16 \) square units 2. **Triangle \( QRS\):** - Base \( QS\): \( |8 - 0| = 8 \) units - Height (from point \( R\) to the line \( QS\)): \( |4 - (-4)| = 8 \) units
Transcribed Image Text:**Question:** Which of the given shapes has a larger area? [Graph Description] - The graph features a coordinate plane with axes labeled \( x \) and \( y \). - The graph spans both positive and negative directions of the \( x \) and \( y \) axes, covering 12 units on the \( x \)-axis and 12 units on the \( y \)-axis. - There are two geometric shapes plotted on the graph: a rectangle \( ABCD \) and a triangle \( QRS \). **Rectangle \( ABCD \):** - Vertex \( A\) is at (0, 2) - Vertex \( B\) is at (4, 2) - Vertex \( C\) is at (4, -2) - Vertex \( D\) is at (0, -2) **Triangle \( QRS \):** - Vertex \( Q\) is at (0, -4) - Vertex \( R\) is at (6, 4) - Vertex \( S\) is at (8, -4) **Options:** - The rectangle - The triangle **Buttons:** - Back - Next **Instructions:** Analyze the shapes \( ABCD \) and \( QRS \) on the graph and determine which shape has a larger area. Select the appropriate option from "the rectangle" or "the triangle" and click the "Next" button to proceed once you have made your selection. **Explanation of Diagram:** - The coordinate plane is divided into a grid with each small square representing one square unit. - The rectangle \( ABCD \) is plotted in the first and fourth quadrants. - The triangle \( QRS \) is plotted in the fourth quadrant and extends into the first quadrant. To determine the areas: 1. **Rectangle \( ABCD\):** - Length: \( |4 - 0| = 4 \) units - Width: \( |2 - (-2)| = 4 \) units - Area: \( 4 \times 4 = 16 \) square units 2. **Triangle \( QRS\):** - Base \( QS\): \( |8 - 0| = 8 \) units - Height (from point \( R\) to the line \( QS\)): \( |4 - (-4)| = 8 \) units
**Question:** What is true about side \( AB \) and side \( AD \)? **Explanation:** The image shows a coordinate plane with a rectangle \( ABCD \) drawn on it. The vertices of the rectangle are labeled as \( A \), \( B \), \( C \), and \( D \). The axes are labeled \( x \) (horizontal) and \( y \) (vertical). - Side \( AB \) is horizontal. - Side \( AD \) is vertical. **Multiple Choice Options:** 1. The slopes are the same. 2. The slopes are the opposite reciprocal. **Graph Details:** - In the coordinate plane, side \( AB \) runs horizontally from left to right. - Side \( AD \) runs vertically from bottom to top. - The rectangle \( ABCD \) is aligned such that side \( AB \) is parallel to the \( x \)-axis and side \( AD \) is parallel to the \( y \)-axis. **Understanding Slopes:** - The slope of a horizontal line (like \( AB \)) is 0. - The slope of a vertical line (like \( AD \)) is undefined. Based on the above details: - The slopes are NOT the same since the slope of \( AB \) is 0 and the slope of \( AD \) is undefined. - The correct statement is: **The slopes are the opposite reciprocal**. **Answer and Navigation Buttons:** - The correct option to select is "The slopes are the opposite reciprocal." - Two navigation buttons are available at the bottom: "Back" and "Next." --- (Buttons) - "Back" & "Next" Choose the correct answer to proceed to the next question.
Transcribed Image Text:**Question:** What is true about side \( AB \) and side \( AD \)? **Explanation:** The image shows a coordinate plane with a rectangle \( ABCD \) drawn on it. The vertices of the rectangle are labeled as \( A \), \( B \), \( C \), and \( D \). The axes are labeled \( x \) (horizontal) and \( y \) (vertical). - Side \( AB \) is horizontal. - Side \( AD \) is vertical. **Multiple Choice Options:** 1. The slopes are the same. 2. The slopes are the opposite reciprocal. **Graph Details:** - In the coordinate plane, side \( AB \) runs horizontally from left to right. - Side \( AD \) runs vertically from bottom to top. - The rectangle \( ABCD \) is aligned such that side \( AB \) is parallel to the \( x \)-axis and side \( AD \) is parallel to the \( y \)-axis. **Understanding Slopes:** - The slope of a horizontal line (like \( AB \)) is 0. - The slope of a vertical line (like \( AD \)) is undefined. Based on the above details: - The slopes are NOT the same since the slope of \( AB \) is 0 and the slope of \( AD \) is undefined. - The correct statement is: **The slopes are the opposite reciprocal**. **Answer and Navigation Buttons:** - The correct option to select is "The slopes are the opposite reciprocal." - Two navigation buttons are available at the bottom: "Back" and "Next." --- (Buttons) - "Back" & "Next" Choose the correct answer to proceed to the next question.
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