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SSAT Middle Level Math : Coordinate Geometry

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Example Questions

Example Question #1 : Coordinate Geometry

Give the slope of the line that passes through (4,2) and (-8,-3) .

Possible Answers:

$\frac{5}{12}$

$-\frac{5}{2}$

$\frac{12}{5}$

$\frac{1}{4}$

$-\frac{2}{5}$

Correct answer:

$\frac{5}{12}$

Explanation:

Use the slope formula, substituting $x_{1}= 4, y_{1}=2,x_{2}= -8, y_{2}=-3$ :

$m =\frac{ y_{2}- y_{1} }{x_{2} - x_{1}}=\frac{ -3-2 }{-8-4} = \frac{ -5 }{-12} = \frac{5 }{12}$

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Example Question #2 : Coordinate Geometry

Give the slope of a line that passes through (5,5) and (2,4) .

Possible Answers:

$\frac{1}{3}$

$\frac{3}{4}$

$\frac{4}{5}$

$\frac{2}{5}$

$\frac{1}{2}$

Correct answer:

$\frac{1}{3}$

Explanation:

Using the slope formula, substituting $x_{1}=5$ , $x_{2}=2$ , $y_{1}=5$ , and $y_{2}=4$ :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{4-5}{2-5}$

Subtract to get:

$m=\frac{-1}{-3}$

Cancel out the negative signs to get:

$m=\frac{1}{3}$

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Example Question #2 : Geometry

Give the slope of a line that passes through (-7,4) and (2,5) .

Possible Answers:

$\frac{2}{9}$

$\frac{3}{8}$

$\frac{5}{7}$

$\frac{1}{9}$

$\frac{4}{7}$

Correct answer:

$\frac{1}{9}$

Explanation:

Using the slope formula with $x_{1}=-7$ , $x_{2}=2$ , $y_{1}=4$ , $y_{2}=5$ :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{5-4}{2-(-7)}$

Subtract to get:

$m=\frac{1}{9}$

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Example Question #3 : Geometry

Give the slope of the line that passes through (-5,3) and (1,9) .

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

$\frac{3}{2}$

$-\frac{3}{4}$

Correct answer:

Explanation:

Using the slope formula for

$x_{1}=-5$ , $x_{2}=1$ , $y_{1}=3$ , and $y_{2}=9$ :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{9-3}{1-(-5)}$

Combine the negative signs to get:

$m=\frac{9-3}{1+5}$

Subtract and add to get:

$m=\frac{6}{6}$

Reduce to get:

m=1

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Example Question #3 : Geometry

Give the slope of a line that passes through (4,7) and (2,3) .

Possible Answers:

$\frac{3}{7}$

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

Using the slope formula, where is the slope, $(x_{1},y_{1})=$ (4,7) , and $(x_{2},y_{2})=$ (2,3) :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{3-7}{2-4}$

$m=\frac{-4}{-2}$

m=2

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Example Question #4 : Geometry

Find the slope of the line that passes through the points (5,-4) and (-5,-4)

Possible Answers:

$\frac{4}{5}$

Cannot be determined

Correct answer:

Explanation:

Using the slope formula, where is the slope, $(x_{1},y_{1})=$ (5,-4) , and $(x_{2},y_{2})=$ (-5,-4) :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{-4-(-4)}{-5-5}$

$m=\frac{-4+4}{-10}$

$m=\frac{0}{-10}$

m=0

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Example Question #3 : Coordinate Geometry

Find the slope of a line with points (-1,0) and (-10, 5) .

Possible Answers:

Cannot be determined

$-\frac{5}{9}$

$\frac{5}9 {}$

$-\frac{9}{5}$

$\frac{9}{5}$

Correct answer:

$-\frac{5}{9}$

Explanation:

Using the slope formula, where is the slope, $(x_{1},y_{1})=$ (-1,0) , and $(x_{2},y_{2})=$ (-10, 5) :

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{5-0}{-10-(-1)}$

$m=\frac{5}{-10+1}$

$m=-\frac{5}{9}$

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

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?

Possible Answers:

$\frac{1}{18}$

$\frac{1}{3}$

$\frac{5}{9}$

$\frac{3}{18}$

Correct answer:

$\frac{1}{3}$

Explanation:

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

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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:

$\left(x_{1},y_{1}\right) = (0,3)$ and $(x_{2}, y_{2})= (18,9)$

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

$m = \frac{9-3}{18-0}}$

This reduces to $\frac{6}{18} =\frac{1}{3}$

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

Triangle2

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

Possible Answers:

$120 \text{ square units}$

$44 \text{ square units}$

$22 \text{ square units}$

$60\text{ square units}$

Correct answer:

$60\text{ square units}$

Explanation:

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

$A = \frac{base \times height}{2}$

Thus, the solution is:

$A = \frac{10 \times 12}{2} = \frac{120}{2} = 60 \text{ square units}$

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

Triangle6

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

Possible Answers:

Correct answer:

Explanation:

Using the coordinate system, one can see the base of the triangle is 6 units in length. Since it is an equilateral triangle, the other two sides must also be 6 units each in length. Therefore the perimeter is:

P = a + b + c = 6 + 6 + 6 = 18

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SSAT Middle Level Math : Coordinate Geometry

Study concepts, example questions & explanations for SSAT Middle Level Math

All SSAT Middle Level Math Resources

Example Questions

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

Example Question #2 : Geometry

Example Question #3 : Geometry

Example Question #3 : Geometry

Example Question #4 : Geometry

Example Question #3 : Coordinate Geometry

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

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

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

All SSAT Middle Level Math Resources

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