# SSAT Middle Level Math : Geometry

## Example Questions

### Example Question #3 : Graphing Points

Which of the following points is in Quadrant II on the coordinate plane?

Explanation:

All points in Quadrant II have negative -coordinates and positive -coordinates. The only answer that fulfills these criteria is

### Example Question #21 : Graphing

In which quadrant or on which axis will we find the point ?

The -axis

The -axis

The -axis

Explanation:

By definition, any point in the coordinate plane that has a non-zero value -coordinate and a zero-value -coordinate is on the -axis.

### Example Question #22 : Graphing

In which quadrant or on which axis of the coordinate plane will you find the point  ?

The -axis

Explanation:

A point with a positive -coordinate and a negative -coordinate can be found in Quadrant IV.

### Example Question #1 : 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 coordinates of the midpoint are .

### 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 is half the sum of the -coordinates of the endpoints:

The -coordinate of the midpoint is found similarly:

The midpoint has coordinates .

### Example Question #21 : Geometry

In which quadrant or on which axis will you find the point ?

The -axis

Explanation:

By definition, a point with a negative -coordinate and a negative -coordinate lies in Quadrant III on the coordinate plane.

### Example Question #1 : How To Find A Square On A Coordinate Plane

The above square has an area of  square units. What fraction of the area of square is in quadrant II?

Explanation:

To find the fraction of the entire squares area that lays in quadrant II, notice that the square is taking up an equivalent amount in each of the four quadrants. Thus,  of the squares area is in quadrant II.

Also note that the area of the square that lays in quadrant II is  square units, thus the problem could have alternatively been solved by reducing .

### Example Question #1 : How To Find A Square On A Coordinate Plane

If a square has an area of  square units, what is the perimeter?

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal

Once you've found the length of side , apply the formula .

Thus, the solution is

### Example Question #2 : How To Find A Square On A Coordinate Plane

A square has an area of  square units, what is the perimeter?

Explanation:

In order to solve this problem, apply the formula , in order to conclude that the length of side  must equal  for the area to equal

Once you've found the length of side , apply the formula

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

Find the perimeter of the square shown above.