# ISEE Middle Level Math : Coordinate Geometry

## Example Questions

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### Example Question #1 : Coordinate Geometry

Which of the following is a vertex of the square?

Explanation:

The coordinates of a point are determined by the distance from the origin. The first point in the ordered pair is the number of units to the left or right of the origin. Negative numbers indicate the number of units to the left while positive numbers indicate the number of units to the right. The second number indicates the number of units above or below the origin. Positive numbers indicate the number of units above while negative numbrs indicate the number of units below the origin. The vertices of the square are:

### Example Question #1 : How To Do Coordinate Geometry

Which of the following points will you find on the -axis?

Explanation:

A point is located on the -axis if and only if it has -coordinate (first coordinate) 0. Of the five choices, only  fits that description.

### Example Question #3 : Coordinate Geometry

Which of the following points is on the -axis?

Explanation:

A point is located on the -axis if and only if it has a -coordinate equal to zero.  So the answer is .

### Example Question #3 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates  and . Give the midpoint of the segment.

Explanation:

The -coordinate of the midpoint can be found by dividing the sum of the -coordinates of the endpoints by 2:

The -coordinate of the midpoints is found similarly:

### Example Question #4 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates  and . Give the coordinates of the midpoint of the segment.

Explanation:

The -coordinate of the midpoint can be found by dividing the sum of the -coordinates of the endpoints by 2:

The -coordinate of the midpoint is found similarly:

.

The correct response is .

### Example Question #5 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates  and .  Give the coordinates of the midpoint of the segment.

Explanation:

The -coordinate of the midpoint is half the sum of the -coordinates of the endpoints:

The -coordinate of the midpoint is found similarly:

The correct response is .

### Example Question #6 : How To Find The Points On A Coordinate Plane

Angela plotted points A through E on the coordinate plane shown below.

Which point is located at the ordered pair

Point D

Point C

Point A

Point E

Point B

Point B

Explanation:

Start at point (0, 0) in the bottom, left corner of the the coordinate plane. From there, count right 2 spaces. This is the first number in the given ordered pair. From that point, count up 8 spaces. This is the second number in the given ordered pair.

By moving right 2 and up 8, you should have found Point B.

### Example Question #4 : Coordinate Geometry

Give the slope of the line that passes through  and .

Explanation:

Use the slope formula, substituting :

### Example Question #5 : Coordinate Geometry

What is the slope of the line that passes through and ?

Explanation:

We can use the slope formula:

### Example Question #6 : Coordinate Geometry

What is the slope of the line that passes through  and ?