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ISEE Middle Level Math : How to find the points on a coordinate plane

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Example Questions

Example Question #1 : How To Do Coordinate Geometry

Which of the following points will you find on the $\displaystyle y$-axis?

Possible Answers:

(30,30) $\displaystyle (30,30)$

$\displaystyle (30,-30)$

$\displaystyle (-30,30)$

(30, 0) $\displaystyle (30, 0)$

(0,-30) $\displaystyle (0,-30)$

Correct answer:

(0,-30) $\displaystyle (0,-30)$

Explanation:

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

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

Which of the following points is on the $\displaystyle x$-axis?

Possible Answers:

(0,10) $\displaystyle (0,10)$

(20,1) $\displaystyle (20,1)$

(20,0) $\displaystyle (20,0)$

(0,20) $\displaystyle (0,20)$

(10,10) $\displaystyle (10,10)$

Correct answer:

(20,0) $\displaystyle (20,0)$

Explanation:

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

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Example Question #1 : Coordinate Geometry

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

Possible Answers:

$\displaystyle (8.66, 6.84)$

$\displaystyle (2.68, 6.84)$

$\displaystyle (2.68 , 3.42 )$

$\displaystyle (8.66, 3.42 )$

Correct answer:

$\displaystyle (8.66, 3.42 )$

Explanation:

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

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

The $\displaystyle y$-coordinate of the midpoints is found similarly:

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

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Example Question #2 : Coordinate Geometry

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

Possible Answers:

$\displaystyle (-250, 250)$

$\displaystyle (-50, 50)$

$\displaystyle (-500, 500)$

$\displaystyle (-100, 100 )$

Correct answer:

$\displaystyle (-250, 250)$

Explanation:

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

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

The $\displaystyle y$-coordinate of the midpoint is found similarly:

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

The correct response is $\displaystyle (-250, 250)$.

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Example Question #4 : Coordinate Geometry

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

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

The $\displaystyle x$-coordinate of the midpoint is half the sum of the $\displaystyle x$-coordinates of the endpoints:

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

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

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

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

$= \frac{20}{3}$ $\displaystyle = \frac{20}{3}$

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

The $\displaystyle y$-coordinate of the midpoint is found similarly:

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

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

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

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

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

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

$= \frac{ 15}{8}$ $\displaystyle = \frac{ 15}{8}$

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

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

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Example Question #282 : 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)? $\displaystyle (2, 8)?$

Possible Answers:

Point B

Point E

Point C

Point D

Point A

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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ISEE Middle Level Math : How to find the points on a coordinate plane

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 : How To Find The Points On A Coordinate Plane

Example Question #1 : Coordinate Geometry

Example Question #2 : Coordinate Geometry

Example Question #4 : Coordinate Geometry

Example Question #282 : Geometry

All ISEE Middle Level Math Resources

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