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ISEE Middle Level Math : Geometry

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Example Questions

Example Question #434 : Problem Solving

Which of the following points is on the -axis?

Possible Answers:

(20,0)

(20,1)

(0,20)

(10,10)

(0,10)

Correct answer:

(20,0)

Explanation:

A point is located on the -axis if and only if it has a -coordinate equal to zero. So the answer is (20,0) .

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Example Question #282 : Geometry

A line segment on the coordinate plane has its endpoints at the points with coordinates (7.32, -3. 16) and (10, 10) . Give the midpoint of the segment.

Possible Answers:

(8.66, 6.84)

(8.66, 3.42 )

(2.68, 6.84)

(2.68 , 3.42 )

Correct answer:

(8.66, 3.42 )

Explanation:

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

$(7.32 + 10) \div 2 = 17.32 \div 2 = 8.66$

The -coordinate of the midpoints is found similarly:

$(-3.16 + 10) \div 2 =(10 -3.16 ) \div 2 = 6.84 \div 2 = 3.42$

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Example Question #1 : Coordinate Geometry

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( - 300, 200 \right )$ and $\left ( -200, 300 \right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

(-100, 100 )

(-50, 50)

(-250, 250)

(-500, 500)

Correct answer:

(-250, 250)

Explanation:

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

$[ -300 + (-200) ] \div 2 = [ -(300 + 200) ] \div 2 = -500 \div 2 = - (500 \div 2) = -250$

The -coordinate of the midpoint is found similarly:

$(200 + 300) \div 2 = 500 \div 2 = 250$ .

The correct response is (-250, 250) .

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Example Question #284 : Geometry

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( 3 \frac{1}{3}, - 1 \frac{1}{2}\right )$ and $\left ( 10, 5 \frac{1}{4}\right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

$\left (6 \frac{2}{3}, 1 \frac{7}{8}\right )$

$\left ( 3 \frac{1}{3}, 3 \frac{3}{8}\right )$

$\left (6 \frac{2}{3}, 6 \frac{3}{4}\right )$

$\left (13 \frac{1}{3}, 3 \frac{3}{4}\right )$

Correct answer:

$\left (6 \frac{2}{3}, 1 \frac{7}{8}\right )$

Explanation:

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

$\frac{1}{2} \times \left ( 3 \frac{1}{3} + 10 \right )$

$= \frac{1}{2} \times 13 \frac{1}{3}$

$= \frac{1}{2} \times \frac{40}{3}$

$= \frac{1}{1} \times \frac{20}{3}$

$= \frac{20}{3}$

$= 6 \frac{1}{3}$

The -coordinate of the midpoint is found similarly:

$\frac{1}{2} \times \left ( - 1 \frac{1}{2} + 5 \frac{1}{4} \right )$

$= \frac{1}{2} \times \left ( 5 \frac{1}{4} - 1 \frac{1}{2} \right )$

$= \frac{1}{2} \times \left ( 5 \frac{1}{4} - 1 \frac{2}{4} \right )$

$= \frac{1}{2} \times \left ( 4 \frac{5}{4} - 1 \frac{2}{4} \right )$

$= \frac{1}{2} \times 3 \frac{3}{4}$

$= \frac{1}{2} \times \frac{15}{4}$

$= \frac{ 15}{8}$

$=1 \frac{7}{8}$

The correct response is $\left (6 \frac{2}{3}, 1 \frac{7}{8}\right )$ .

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Example Question #281 : Geometry

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

Points_grid

Which point is located at the ordered pair (2, 8)?

Possible Answers:

Point D

Point C

Point A

Point B

Point E

Correct answer:

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.

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Example Question #2 : Coordinate Geometry

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

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$-\frac{1}{3}$

Correct answer:

$-\frac{1}{3}$

Explanation:

Use the slope formula, substituting $x_{1}= 5, y_{1}=3,x_{2}= -1, y_{2}=5$ :

$m =\frac{ y_{2}- y_{1} }{x_{2} - x_{1}}=\frac{ 5-3 }{-1-5} = \frac{ 2 }{-6} =-\frac{1 }{3}$

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Example Question #282 : Geometry

What is the slope of the line that passes through (4,4) and (8,8) ?

Possible Answers:

1.5

0.5

2.5

Correct answer:

Explanation:

We can use the slope formula:

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

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Example Question #6 : Coordinate Geometry

What is the slope of the line that passes through (4,7) and (-3,-7) ?

Possible Answers:

1.5

3.5

Correct answer:

Explanation:

We can use the slope formula:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-7-7}{-3-4}=\frac{-14}{-7}=2$

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

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

Possible Answers:

m = -2

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

m = 2

$m= -\frac{1}{12}$

Correct answer:

$m= -\frac{1}{12}$

Explanation:

The formula for slope is:

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

In this particular question our values are given as follows.

$y_{2} = -4$

$y_{1} =-3$

$x_{2} = 8$

$x_{1} = -4$

Substituting the above values into the formula for slope we get,

$\frac{-4 - (-3)}{8- (-4)} = \frac{-1}{12}$

$m = -\frac{1}{12}$ .

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Example Question #436 : Problem Solving

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:

$\frac{3}{18}$

$\frac{5}{9}$

$\frac{1}{3}$

$\frac{1}{18}$

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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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #434 : Problem Solving

Example Question #282 : Geometry

Example Question #1 : Coordinate Geometry

Example Question #284 : Geometry

Example Question #281 : Geometry

Example Question #2 : Coordinate Geometry

Example Question #282 : Geometry

Example Question #6 : Coordinate Geometry

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

Example Question #436 : Problem Solving

All ISEE Middle Level Math Resources

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