Integers and coordinates

Opposite numbers have the same absolute value and opposite signs. Their sum is 0. For example, the opposite of −7 is 7, and the opposite of 7 is −7.

For numbers with the same sign, add their absolute values and keep the sign. For different signs, subtract the smaller absolute value from the larger and keep the sign of the number with the larger absolute value. For example, −8 + 3 = −5.

The fourth vertex is vertically aligned with A and horizontally aligned with C.

Moving right increases the first coordinate; moving down decreases the second. Apply the two changes separately.

Subtracting a number means adding its opposite: a − b = a + (−b). Subtracting a negative therefore becomes addition. For example, −4 − (−7) = −4 + 7 = 3.

On a number line, the greater number is farther right. A positive number is greater than a negative number; of two negative numbers, the one closer to zero is greater. For example, −3 > −8. Use = for equal numbers.

Reflecting across the y-axis changes the sign of the first coordinate and leaves the second unchanged.

Locate zero and find the value of one interval from the labelled numbers. Count intervals from zero to A: numbers on the right are positive and those on the left are negative.

The quadrant of a point (x, y) depends on the signs of its two coordinates. You do not need to calculate its exact distance from the axes.

1. Look at the first coordinate, x: a positive value means right of the y-axis; a negative value means left.
2. Look at the second coordinate, y: a positive value means above the x-axis; a negative value means below.
3. Combine the two directions and find the corresponding quadrant in the diagram.

Remember: I: (+, +), II: (−, +), III: (−, −), IV: (+, −). In each sign pair, the first sign belongs to x and the second to y.

Quadrants are numbered counterclockwise, starting at the upper right. If either coordinate is 0, the point lies on an axis or at the origin and does not belong to any quadrant.

When one coordinate is shared, the length is the absolute difference of the other coordinates. A distance cannot be negative.