GED Math : Coordinate Geometry

Example Questions

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Example Question #1 : Points And Coordinates

Refer to the above diagram. Give the coordinates of the plotted point.

Explanation:

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 .

Example Question #1 : Points And Coordinates

Refer to the above diagram. Give the coordinates of the plotted point.

Explanation:

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 .

Example Question #1 : Points And Coordinates

Refer to the above diagram.

Which of the following points has coordinates ?

Explanation:

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 .

Example Question #4 : Points And Coordinates

Refer to the above diagram.

Which of the following points has coordinates ?

Explanation:

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 .

Example Question #1 : Points And Coordinates

At what point do the lines  and  intersect?

Explanation:

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.

Example Question #2 : Points And Coordinates

The slope of a given line is . If one of the points that the line goes through is , which of the following can also be a point on the same line?

Explanation:

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.

Example Question #7 : Points And Coordinates

Explanation:

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 .

Example Question #1 : Points And Coordinates

Which of the following gives the coordinates of a point on the line of the equation  ?

Explanation:

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:

:

:

Example Question #1 : Points And Coordinates

In which quadrant is the point located in the coordinate plane?

Explanation:

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.

Example Question #1 : Coordinate Geometry

Which of the following points occurs on the line given by

Explanation:

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)