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Q64.

Expert-verified

Pre-algebra

Found in: Page 52

Book edition Common Core Edition

Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff

Pages 183 pages

ISBN 9780547587776

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Short Answer

Plot the point in a coordinate plane. Describe the location of the point.
$E (4, - 2)$

Point $E (4, - 2)$ is 4 units right from the origin and 2 units down from the x-axis. Point $E (4, - 2)$ is in Quadrant IV.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. What is a coordinate system?

A Rectangular or Cartesian coordinate system in two dimensions (x and y) is defined by an ordered pair of perpendicular lines or axes

Points are placed by their distance along a horizontal (x) and vertical (y) axis from the origin, defined as (0, 0).

Coordinate of the Origin

It has zero distance from both the axes. Hence the coordinates of the origin are (0, 0).

Sign convention of all quadrants:

First quadrant: x – positive and y – positive

2^nd quadrant: x – negative and y – positive

3^rd quadrant: x – negative and y – negative

4^th quadrant: x – positive and y – negative

Step 2. Coordinate Geometry in Two Dimensional Plane.

In coordinate geometry, first, we learn about locating the points in a X – Y coordinate plane.

For example, the point (2, 3) is 3 units away from the X−axis measured along the positive X−axis and 2 units away from Y−axis measured along the positive Y−axis.

The points having x-coordinate as ‘0′ lies on the Y−axis and the points having Y-coordinate as ‘0’ lies on the X−axis

For example, the points (2, 0), (5, 0) lies on X−axis and the points (0, −3), (0, 7) lies on Y−axis

Step 3. Plot the point in a coordinate plane. Describe the location of the point.

Consider, the point provided in the question, $E (4, - 2)$

Point $E (4, - 2)$ is 4 units right from the origin and 2 units down from the x-axis.

Point $E (4, - 2)$ is in Quadrant VI.

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