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Q64.

Expert-verified
Found in: Page 52

### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776

# Plot the point in a coordinate plane. Describe the location of the point. $\text{E} \text{(}4\text{,} -2\text{)}$

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

See the step by step solution

## 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).

First quadrant: x – positive and y – positive

2nd quadrant: x – negative and y – positive

3rd quadrant: x – negative and y – negative

4th 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, $E \left( 4, -2 \right)$

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

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