SSAT Middle Level Math : Coordinate Geometry
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Example Questions
Example Question #11 : Coordinate Geometry
The isosceles triangle shown above has a perimeter of 22 and base of 6. Find the lengths of the left and right sides, respectively. Assume no other side has a length of 6.
With a perimeter of 22 and base of 6, this means the other two sides must add up to:
Because an isosceles triangle must have two sides equal in length and we know from the problem that no other side equals 6, the two remaining sides must be equal to each other.
Thus, to be equal to each other and also add up to 16, each side must be 8 units in length.
Example Question #4 : How To Find A Triangle On A Coordinate Plane
Given the above triangle has a base of 5 and height of 6, what is the perimeter of the triangle?
First, use the Pythagorean Theorem to find the length of the hypotenuse:
Thus,
Finally, the perimeter is the sum of the sides of the triangle or:
Example Question #1 : How To Find A Triangle On A Coordinate Plane
Given triangle 
To find the area of this triangle, we first need to determine the length of sides AB and BC. First, point B shares the same x-coordinate as point A and the same y-coordinate as point C. Thus, B must be located at point (-2,-2).
The length of side AB must then be:
and the length of side BC:
Using the area formula,
we can find the area using the base (side BC) and height (side AB):
Example Question #6 : How To Find A Triangle On A Coordinate Plane
Given triangle 
Use the Pythagorean Theorem to find the length of side AC:
Then, the perimeter is simply the sum of all three sides:
Example Question #7 : How To Find A Triangle On A Coordinate Plane
The above triangle has base 6 and height 4. Find the perimeter.
Because the y-axis bisects the base, we can divide the triangle into two, equal right triangles. The base of the right triangle is thus half that of the larger triangle, or 3. The height is still 4. To find the hypotenuse, use the Pythagorean Theorem:
Thus, we now know the base as given in the problem and each of the other two sides (which are also the hypotenuses of the right triangles).
Therefore, the perimeter is:
Example Question #1 : How To Find A Triangle On A Coordinate Plane
Given a height of 
The area of any triangle is calculated by the formula:
Thus, the area of this triangle is:
Example Question #1 : How To Find A Triangle On A Coordinate Plane
Given the above triangle has a base of 
Use the Pythagorean Theorem,
where 
Rearranging to solve for the height, 
Example Question #1 : Graphing Points
Which of the following points would be located in Quadrant III?
By definition, a point on the coordinate plane that is in Quadrant III must have both a negative 
Example Question #2 : Graphing Points
In which quadrant or on what axis will you find the point 
Quadrant I
Quadrant III
The 
Quadrant II
Quadrant IV
Quadrant II
The point 
Example Question #1 : Graphing Points
In which quadrant or on which axis will you find the point 
Quadrant I
Quadrant II
The 
Quadrant III
The 
The
The point 
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All SSAT Middle Level Math Resources
