/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 35 Plot each point. Then plot the p... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 35

Plot each point. Then plot the point that is symmetric to it with respect to (a) the \(x\) -axis; (b) the y-axis; (c) the origin. $$ (5,-2) $$

Short Answer

Expert verified
The symmetric points are: (5, 2); (-5, -2); (-5, 2).

Step by step solution

01

- Plot the Point (5, -2)

On the coordinate plane, locate the point (5, -2). This means to move 5 units to the right along the x-axis and 2 units down along the y-axis.
02

- Find the Symmetric Point with respect to the x-axis

To find the point symmetric to (5, -2) with respect to the x-axis, change the sign of the y-coordinate while keeping the x-coordinate the same. The new point is (5, 2).
03

- Plot the Point (5, 2)

On the coordinate plane, locate the point (5, 2). This means to move 5 units to the right along the x-axis and 2 units up along the y-axis.
04

- Find the Symmetric Point with respect to the y-axis

To find the point symmetric to (5, -2) with respect to the y-axis, change the sign of the x-coordinate while keeping the y-coordinate the same. The new point is (-5, -2).
05

- Plot the Point (-5, -2)

On the coordinate plane, locate the point (-5, -2). This means to move 5 units to the left along the x-axis and 2 units down along the y-axis.
06

- Find the Symmetric Point with respect to the Origin

To find the point symmetric to (5, -2) with respect to the origin, change the signs of both the x-coordinate and the y-coordinate. The new point is (-5, 2).
07

- Plot the Point (-5, 2)

On the coordinate plane, locate the point (-5, 2). This means to move 5 units to the left along the x-axis and 2 units up along the y-axis.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Plotting Points
Plotting points on a coordinate plane is the foundation of understanding geometry and algebra. Each point has an x-coordinate and a y-coordinate. The x-coordinate tells you how far to move to the right (positive) or left (negative) along the x-axis, and the y-coordinate tells you how far to move up (positive) or down (negative) along the y-axis.
For example, to plot the point (5, -2):
  • Move 5 units to the right along the x-axis.
  • Then move 2 units down along the y-axis.
This should place you at the point (5, -2). Making sure you accurately plot points is crucial for understanding further concepts like symmetry.
Coordinate Plane
The coordinate plane, also known as the Cartesian plane, consists of two perpendicular lines called axes that intersect at a point called the origin. Typically, the horizontal line is the x-axis, and the vertical line is the y-axis.
Here are some key things to remember about the coordinate plane:
  • The origin, where the x-axis and y-axis intersect, is labeled as (0,0).
  • The plane is divided into four quadrants:
  • Quadrant I: Positive x and positive y coordinates.
  • Quadrant II: Negative x and positive y coordinates.
  • Quadrant III: Negative x and negative y coordinates.
  • Quadrant IV: Positive x and negative y coordinates.
Understanding the coordinate plane is essential for plotting points and studying their symmetry.
Symmetry
Symmetry in coordinate geometry refers to the balanced and proportional arrangement of points based on certain lines or points. Here are the types of symmetry you need to know:
  • Symmetry about the x-axis: To find a point symmetric about the x-axis, change the sign of the y-coordinate, keeping the x-coordinate the same. For example, the point symmetric to (5, -2) is (5, 2).
  • Symmetry about the y-axis: To find a point symmetric about the y-axis, change the sign of the x-coordinate, keeping the y-coordinate the same. For example, the point symmetric to (5, -2) is (-5, -2).
  • Symmetry about the origin: To find a point symmetric about the origin, change the signs of both the x-coordinate and the y-coordinate. For example, the point symmetric to (5, -2) is (-5, 2).
Practicing finding symmetrical points helps solidify your understanding of the coordinate plane and enhances your spatial reasoning.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Kinetic Energy The kinetic energy \(K\) of a moving object varies directly with its mass \(m\) and the square of its velocity \(v\). If an object weighing 25 kilograms and moving with a velocity of 10 meters per second has a kinetic energy of 1250 joules, find its kinetic energy when the velocity is 15 meters per second.

Based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam. A square with an area of 64 square meters is inscribed inside a circle. What are the circumference and area of the circle?

Simplify: \(\left(\frac{4}{25}\right)^{3 / 2}\)

Driving to School The time \(t\) that it takes to get to school varies inversely with your average speed \(s\). (a) Suppose that it takes you 40 minutes to get to school when your average speed is 30 miles per hour. Express the driving time to school in terms of average speed. (b) Suppose that your average speed to school is 40 miles per hour. How long will it take you to get to school?

The weight of a body above the surface of Earth varies inversely with the square of the distance from the center of Earth. If a certain body weighs 55 pounds when it is 3960 miles from the center of Earth, how much will it weigh when it is 3965 miles from the center?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.