SSAT Middle Level Math : Coordinate Geometry

Example Questions

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Example Question #1 : Geometry

Give the slope of the line that passes through  and .

Explanation:

Use the slope formula, substituting :

Example Question #1 : Coordinate Geometry

Give the slope of a line that passes through  and .

Explanation:

Using the slope formula, substituting , and :

Subtract to get:

Cancel out the negative signs to get:

Example Question #1 : Geometry

Give the slope of a line that passes through  and .

Explanation:

Using the slope formula with , :

Subtract to get:

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

Give the slope of the line that passes through  and .

Explanation:

Using the slope formula for

, and :

Combine the negative signs to get:

Reduce to get:

Example Question #2 : Geometry

Give the slope of a line that passes through  and .

Explanation:

Using the slope formula, where  is the slope,  , and  :

Example Question #1 : Geometry

Find the slope of the line that passes through the points  and

Cannot be determined

Explanation:

Using the slope formula, where  is the slope,  , and   :

Example Question #1 : Coordinate Geometry

Find the slope of a line with points  and .

Cannot be determined

Explanation:

Using the slope formula, where  is the slope,  , and   :

Example Question #1 : Geometry

Billy set up a ramp for his toy cars. He did this by taking a wooden plank and putting one end on top of a brick that was 3 inches high. He then put the other end on top of a box that was 9 inches high. The bricks were 18 inches apart. What is the slope of the plank?

Explanation:

The value of the slope (m) is rise over run, and can be calculated with the formula below:

The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.

The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.

From this information we know that we can assign the following coordinates for the equation:

and

Below is the solution we would get from plugging this information into the equation for slope:

This reduces to

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

Find the area of the above triangle, given that it has a height of 12 and a base of 10.

Explanation:

Because this is a right triangle, the area formula is simply:

Thus, the solution is:

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

Given the above triangle is an equilateral triangle, find the perimeter in units as drawn in the coordinate system.