Calculate the slope of each side: **Understanding Parallelograms on a Coordinate Plane**This image presents a geometrical figure, specifically a parallelogram, plotted on a coordinate plane. The parallelogram is defined by four vertices labeled A, B, C, and D, connected by straight lines.**Vertices Coordinates:**- Point A is located at (-4, 3).- Point B is at (1, 6).- Point C is at (6, 4).- Point D is at (1, 1).**Axes Information:**- The x-axis and y-axis are denoted, with intervals marked from -7 to 9 on the x-axis and -4 to 11 on the y-axis.**Graph Details:**- The plane uses a grid pattern to facilitate visualization and measurement.- Each unit on both axes is represented by increments of 1.**Parallelogram Properties:**- Opposite sides of the parallelogram are parallel and equal in length.- This figure illustrates the concept of translation and vector addition in coordinate geometry. The parallelogram shows how vectors can represent the sides and diagonals.**Area Calculation:**The area of a parallelogram on the coordinate plane can be calculated using the determinant of a matrix composed of the vertices' coordinates. The area is found using the following formula given vertices $(x_1,y_1), (x_2,y_2), (x_3,y_3), (x_4,y_4)$:\[Area = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - y_1x_2 - y_2x_3 - y_3x_4 - y_4x_1 \right|In our case :\left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - y_1x_2 - y_2x_3 - y_3x_4 - y_4x_1 \right|= \left| -4*6 + 1*4 + 6*1 + 1*3 - (3*1 + 6*6 + 4*1 + 1*-4) \right|= \left| -24 + ### Exercise: Slope Calculation and Polygon Classification#### Question B: Calculate the slope of each side:| $ m_{AB} $ | $ m_{AD} $ ||--------------|--------------|| | || $ m_{DC} $ | $ m_{BC} $ ||--------------|--------------|| | |#### 2. Classify the polygon with the most specific classification you can justify.________________________#### 3. Find the perimeter of your figure to the nearest tenth.________________________### Instructions for Students:1. **Calculate the Slope of Each Side:** - Use the slope formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $ to find the slopes of sides $ AB $, $ AD $, $ DC $, and $ BC $. - Record your slope calculations in the provided table.2. **Classify the Polygon:** - Analyze the slopes calculated above and determine the most specific classification of the polygon (e.g., rectangle, square, trapezoid). - Provide a written justification for your classification in the space provided.3. **Find the Perimeter:** - Measure or calculate the lengths of each side using the distance formula if the coordinates of the vertices are given. - Sum the lengths of all sides to find the perimeter. - Round your final answer to the nearest tenth.### Tips:- Ensure your calculations for slope are accurate to confirm the correct classification of the polygon.- Review geometric properties of polygons to aid in correct classification.- Double-check your arithmetic when calculating the perimeter to ensure precision.

We are given with the graph and need to find the slope

Answered: Calculate the slope of each side

Math

Geometry

Calculate the slope of each side

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: Find the slope and y-intercept of: y=-7x-27

Q: Find the slope of each line : y=8

A: Given: Line: y=8

Q: Graph this line using the slope and y-intercept: у %3D 9х — 5

A: Given equation of line is y=9x-5. The general equation of line in slope intercept form is y=mx+c…

Q: :

Concept explainers

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Question

Calculate the slope of each side:

**Understanding Parallelograms on a Coordinate Plane**

This image presents a geometrical figure, specifically a parallelogram, plotted on a coordinate plane. The parallelogram is defined by four vertices labeled A, B, C, and D, connected by straight lines.

**Vertices Coordinates:**
- Point A is located at (-4, 3).
- Point B is at (1, 6).
- Point C is at (6, 4).
- Point D is at (1, 1).

**Axes Information:**
- The x-axis and y-axis are denoted, with intervals marked from -7 to 9 on the x-axis and -4 to 11 on the y-axis.

**Graph Details:**
- The plane uses a grid pattern to facilitate visualization and measurement.
- Each unit on both axes is represented by increments of 1.

**Parallelogram Properties:**
- Opposite sides of the parallelogram are parallel and equal in length.
- This figure illustrates the concept of translation and vector addition in coordinate geometry. The parallelogram shows how vectors can represent the sides and diagonals.

**Area Calculation:**
The area of a parallelogram on the coordinate plane can be calculated using the determinant of a matrix composed of the vertices' coordinates. The area is found using the following formula given vertices $(x_1,y_1), (x_2,y_2), (x_3,y_3), (x_4,y_4)$:
\[
Area = \frac{1}{2} \left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - y_1x_2 - y_2x_3 - y_3x_4 - y_4x_1 \right|
In our case :
\left| x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1 - y_1x_2 - y_2x_3 - y_3x_4 - y_4x_1 \right|
= \left| -4*6 + 1*4 + 6*1 + 1*3 - (3*1 + 6*6 + 4*1 + 1*-4) \right|
= \left| -24 +

### Exercise: Slope Calculation and Polygon Classification

#### Question B: Calculate the slope of each side:

| $ m_{AB} $ | $ m_{AD} $ |
|--------------|--------------|
| | |

| $ m_{DC} $ | $ m_{BC} $ |
|--------------|--------------|
| | |

#### 2. Classify the polygon with the most specific classification you can justify.
________________________

#### 3. Find the perimeter of your figure to the nearest tenth.
________________________

### Instructions for Students:

1. **Calculate the Slope of Each Side:**
- Use the slope formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $ to find the slopes of sides $ AB $, $ AD $, $ DC $, and $ BC $.
- Record your slope calculations in the provided table.

2. **Classify the Polygon:**
- Analyze the slopes calculated above and determine the most specific classification of the polygon (e.g., rectangle, square, trapezoid).
- Provide a written justification for your classification in the space provided.

3. **Find the Perimeter:**
- Measure or calculate the lengths of each side using the distance formula if the coordinates of the vertices are given.
- Sum the lengths of all sides to find the perimeter.
- Round your final answer to the nearest tenth.

### Tips:
- Ensure your calculations for slope are accurate to confirm the correct classification of the polygon.
- Review geometric properties of polygons to aid in correct classification.
- Double-check your arithmetic when calculating the perimeter to ensure precision.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Points, Lines and Planes$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.