Question

The coordinates of four points are given in absolute terms (all values positive). Plot and label each point in the quadrant requested. Different quadrants will require changing the signs of some or all the coordinates. Point A: Plot the point with absolute coordinates of \((3,6)\) in the third quadrant. Point B: Plot the point with absolute coordinates of \((5,5)\) in the second quadrant. Point C: Plot the point with absolute coordinates of \((2,7)\) in the third quadrant. Point D: Plot the point with absolute coordinates of \((5,9)\) in the fourth quadrant.

Short answer

A: (-3, -6), B: (-5, 5), C: (-2, -7), D: (5, -9)

Step-by-step solution

Understand the Quadrants

The coordinate plane is divided into four quadrants:1. First Quadrant: Both x and y coordinates are positive.2. Second Quadrant: x coordinate is negative, y coordinate is positive.3. Third Quadrant: Both x and y coordinates are negative.4. Fourth Quadrant: x coordinate is positive, y coordinate is negative.

Plot Point A in the Third Quadrant

Point A has absolute coordinates \(3, 6\). In the third quadrant, both coordinates need to be negative. Therefore, Point A should be plotted at \((-3, -6)\).

Plot Point B in the Second Quadrant

Point B has absolute coordinates \(5, 5\). In the second quadrant, the x coordinate is negative, and the y coordinate is positive. Therefore, Point B should be plotted at \((-5, 5)\).

Plot Point C in the Third Quadrant

Point C has absolute coordinates \(2, 7\). In the third quadrant, both coordinates need to be negative. Therefore, Point C should be plotted at \((-2, -7)\).

Plot Point D in the Fourth Quadrant

Point D has absolute coordinates \(5, 9\). In the fourth quadrant, the x coordinate is positive, and the y coordinate is negative. Therefore, Point D should be plotted at \((5, -9)\).

Key concepts

plotting points in quadrants

Plotting points on a coordinate plane involves placing points in one of the four quadrants based on their coordinates. Each quadrant has specific rules for how coordinates are assigned. Getting this right is fundamental for accurate plot placement.

coordinate signs by quadrant

The coordinate plane is divided into four quadrants, and each has unique sign rules for the x and y coordinates: First Quadrant: Both x and y coordinates are positive. Second Quadrant: x-coordinate is negative, but y-coordinate is positive. Third Quadrant: Both x and y coordinates are negative. Fourth Quadrant: x-coordinate is positive, but y-coordinate is negative. Understanding these sign rules is crucial for plotting points correctly in each quadrant.
Let's explore a couple of examples to solidify your understanding. Consider Point A located at (3,6). To plot it in the third quadrant, both signs change to negative, making the coordinates (-3,-6). Similarly, for Point B at (5,5) in the second quadrant, only the x-coordinate changes to negative, resulting in (-5,5). With this knowledge, determining the correct signs for coordinates becomes second nature.

graphing coordinates

Graphing coordinates involves marking points on the coordinate plane at the intersections of the x and y values, which are represented as \((x, y)\). Start by identifying the x-value on the horizontal axis and the y-value on the vertical axis.
Here’s an illustrative walk-through of our given points:

• Point A: Original coordinates \((3, 6)\). For the third quadrant, change both x and y to negative, so Point A becomes \((-3, -6)\).
• Point B: Original coordinates \((5, 5)\). For the second quadrant, only x becomes negative, hence \((-5, 5)\).
• Point C: Original coordinates \((2, 7)\). In the third quadrant, both coordinates become negative, so it turns into \((-2, -7)\).
• Point D: Original coordinates \((5, 9)\). For the fourth quadrant, y becomes negative, thus resulting in \((5, -9)\).

Always double-check the quadrant and ensure you’ve applied the correct signs before plotting.