Integers and the coordinate plane

Front

What are integers?

Back

Integers are whole numbers that can be positive, negative, or zero. They do not include fractions or decimals.

Front

What is the coordinate plane?

Back

The coordinate plane is a two-dimensional surface formed by the intersection of a horizontal line (x-axis) and a vertical line (y-axis). Each point on the plane is defined by an ordered pair (x, y).

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. For example, the absolute value of -3 is 3.

Front

In which quadrant does the point (3, -2) lie?

Back

The point (3, -2) lies in Quadrant IV, where x is positive and y is negative.

Front

What is the distance formula between two points (x1, y1) and (x2, y2)?

Back

The distance formula is: Distance = √((x2 - x1)² + (y2 - y1)²).

Front

How do you find the coordinates of a point after moving a certain distance?

Back

To find the new coordinates, add or subtract the distance from the original coordinates. For example, moving 3 units east from (-6, 4) gives (-3, 4).

Front

What is the value of | -4 |?

Back

The value of | -4 | is 4, as absolute value measures distance from zero.

Front

What is the significance of the x-axis and y-axis in the coordinate plane?

Back

The x-axis is the horizontal line, and the y-axis is the vertical line. They intersect at the origin (0,0) and help define the position of points.

Front

What are the coordinates of the origin in the coordinate plane?

Back

The coordinates of the origin are (0, 0).

Front

What does it mean for a point to be in Quadrant I?

Back

In Quadrant I, both x and y coordinates are positive. For example, the point (2, 3) is in Quadrant I.