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ISEE Middle Level Math : Coordinate Geometry

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Example Questions

Example Question #1 : How To Do Coordinate Geometry

Which of the following is a vertex of the square?

Question_12

Possible Answers:

$\small (-2,1)$

$\small (2,4)$

$\small (-1,2)$

$\small (-1,-4)$

$\small (1,-4)$

Correct answer:

$\small (-1,2)$

Explanation:

The coordinates of a point are determined by the distance from the origin. The first point in the ordered pair is the number of units to the left or right of the origin. Negative numbers indicate the number of units to the left while positive numbers indicate the number of units to the right. The second number indicates the number of units above or below the origin. Positive numbers indicate the number of units above while negative numbrs indicate the number of units below the origin. The vertices of the square are:
$\small (-1,2); (-1,4); (1,2); (-1,4)$

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Example Question #1 : Coordinate Geometry

Which of the following points will you find on the -axis?

Possible Answers:

(30,30)

(-30,30)

(0,-30)

(30, 0)

(30,-30)

Correct answer:

(0,-30)

Explanation:

A point is located on the -axis if and only if it has -coordinate (first coordinate) 0. Of the five choices, only (0,-30) fits that description.

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Example Question #2 : Coordinate Geometry

Which of the following points is on the -axis?

Possible Answers:

(20,1)

(20,0)

(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 #1 : How To Find The Points On A Coordinate Plane

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 B

Point E

Point A

Point C

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 #1 : 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 #2 : Coordinate Geometry

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

Possible Answers:

0.5

2.5

1.5

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 #3 : 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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ISEE Middle Level Math : Coordinate Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1 : How To Do Coordinate Geometry

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

Example Question #282 : Geometry

Example Question #1 : Coordinate Geometry

Example Question #284 : Geometry

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

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

Example Question #3 : Coordinate Geometry

All ISEE Middle Level Math Resources

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