Points and Coordinates - GED Math

Quadrant III of the rectangular coordinate plane comprises the set of points with its - and -coordinates both negative. Therefore, and must both be negative numbers.

If , then , as the product of a positive number and a negative number, must be a negative number. If , then , as the product of two negative numbers, must be a positive number.

For the same reasons, if then is a negative number, and if , then is a positive number.

For to be in Quadrant III, the only correct choice given would be that and .

The point can be reached from the origin by moving negative 2 units horizontally - that is, 2 to the left - then negative 4 units vertically - that is, 4 units down. This is point .

The point can be reached from the origin by moving 4 units horizontally in a positive direction - that is, 4 units to the right - then 2 units vertically in a positive direction - that is, 2 units up. This is point .

The point can be reached from the origin by moving to the right 7 units, making 7 the -coordinate. All points on the -axis, such as this one, have -coordinate 0. That makes this point's coordinates .

The point can be reached from the origin by moving left 7 units, making the first coordinate nagative 7, and up 3 units, making the second coordinate positive 3. The correct coordinates are .

For each point, substitute the first coordinate, or -coordinate, for , and the second coordinate, or -coordinate, for in the equation. This is done with to show that this is the correct choice:

By order of operations, work the left multiplication first:

Work the right multiplication next:

Subtract last:

The ordered pair makes the equality true, so it is the correct choice.

As for the other three, we can work the same steps to demonstrate that each other ordered pair makes the equation incorrect, and, consequently, each is an incorrect choice:

:

:

:

Recall how to find the slope of a line:

Since we already have the slope of the line and one coordinate on the line, we will just need to plug in the given answer choices to see which one would give us the correct slope.

Using the coordinate , we would get the following slope:

must be a point on the given line.

The four quadrants are numbered from I to IV beginning with the upper right quadrant and going counterclockwise. Quadrant IV comprises the points with positive x-coordinate and negative y-coordinate, such as the point ; this is the correct quadrant.

Which of the following points occurs on the line given by

We can find this answer by plugging in our points one by one and finding which point "fits."

Given these points:

Now, we could plug in each point and be super methodical, or we could use a little strategy. On most tests, you will have a time limit. To make the most of your time, start with the easier options.

In this case, try the options with zeroes first. Zeroes tend to cancel things out quickly, and thus are easy to work with. Let's test (0,0)

So, (0,0) is out.

Next, try (6,0)

So, (6,0) is our answer.

Recall that at a point of intersection of two lines, they will have the same x and y-coordinates.

Thus, we can set the two equations equal to each other and solve for to find the x-coordinate.

To find the y-coordinate, plug the back into either of the equations.

Quadrant III of the rectangular coordinate plane comprises the set of points with its - and -coordinates both negative. Therefore, and must both be negative numbers.

If , then , as the product of a positive number and a negative number, must be a negative number. If , then , as the product of two negative numbers, must be a positive number.

For the same reasons, if then is a negative number, and if , then is a positive number.

For to be in Quadrant III, the only correct choice given would be that and .

The point can be reached from the origin by moving negative 2 units horizontally - that is, 2 to the left - then negative 4 units vertically - that is, 4 units down. This is point .

The point can be reached from the origin by moving 4 units horizontally in a positive direction - that is, 4 units to the right - then 2 units vertically in a positive direction - that is, 2 units up. This is point .

The point can be reached from the origin by moving to the right 7 units, making 7 the -coordinate. All points on the -axis, such as this one, have -coordinate 0. That makes this point's coordinates .

The point can be reached from the origin by moving left 7 units, making the first coordinate nagative 7, and up 3 units, making the second coordinate positive 3. The correct coordinates are .

For each point, substitute the first coordinate, or -coordinate, for , and the second coordinate, or -coordinate, for in the equation. This is done with to show that this is the correct choice:

By order of operations, work the left multiplication first:

Work the right multiplication next:

Subtract last:

The ordered pair makes the equality true, so it is the correct choice.

As for the other three, we can work the same steps to demonstrate that each other ordered pair makes the equation incorrect, and, consequently, each is an incorrect choice:

:

:

:

Recall how to find the slope of a line:

Since we already have the slope of the line and one coordinate on the line, we will just need to plug in the given answer choices to see which one would give us the correct slope.

Using the coordinate , we would get the following slope:

must be a point on the given line.

The four quadrants are numbered from I to IV beginning with the upper right quadrant and going counterclockwise. Quadrant IV comprises the points with positive x-coordinate and negative y-coordinate, such as the point ; this is the correct quadrant.

Which of the following points occurs on the line given by

We can find this answer by plugging in our points one by one and finding which point "fits."

Given these points:

Now, we could plug in each point and be super methodical, or we could use a little strategy. On most tests, you will have a time limit. To make the most of your time, start with the easier options.

In this case, try the options with zeroes first. Zeroes tend to cancel things out quickly, and thus are easy to work with. Let's test (0,0)

So, (0,0) is out.

Next, try (6,0)

So, (6,0) is our answer.