### All GED Math Resources

## Example Questions

### Example Question #1 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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.

**Possible Answers:**

**Correct answer:**

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 : Coordinate Geometry

Refer to the above diagram.

Which of the following points has coordinates ?

**Possible Answers:**

**Correct answer:**

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 #1 : Points And Coordinates

Refer to the above diagram.

Which of the following points has coordinates ?

**Possible Answers:**

**Correct answer:**

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 #5 : Coordinate Geometry

At what point do the lines and intersect?

**Possible Answers:**

**Correct 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.

### Example Question #1 : Coordinate Geometry

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?

**Possible Answers:**

**Correct answer:**

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 : Coordinate Geometry

**Possible Answers:**

**Correct answer:**

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 #8 : Coordinate Geometry

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

**Possible Answers:**

**Correct answer:**

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 : Coordinate Geometry

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

**Possible Answers:**

Quadrant I

Quadrant IV

Quadrant II

Quadrant III

**Correct answer:**

Quadrant IV

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

**Possible Answers:**

**Correct answer:**

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.

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