ISEE Lower Level Math : Geometry

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

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Example Questions

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

What are the coordinates for point B?

Possible Answers:

(7, 2)

(2, 8)

(8, 8)

(8, 2)

(2, 7)

Correct answer:

(2, 8)

Explanation:

Begin at point (0, 0) in the bottom left hand corner of the coordinate plane. From there, count the number of spaces you move to the right to line up with Point B. This will be the first number in the ordered pair. Next, count the number of spaces to move up until you reach Point B. This will be the second number in your ordered pair.  

 

You should have counted 2 spaces to the right and 8 spaces up. The ordered pair for Point B is (2, 8).

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

What are the coordinates for Point A?

Possible Answers:

(1, 6)

(6, 0)

(0, 6)

(0, 5)

(6, 1)

Correct answer:

(0, 6)

Explanation:

Begin at point (0, 0) in the bottom left hand corner of the coordinate plane. From there, count the number of spaces you move to the right to line up with Point A. This will be the first number in the ordered pair. Next, count the number of spaces to move up until you reach Point A. This will be the second number in your ordered pair.  

You should have counted 0 spaces to the right and 6 spaces up. The ordered pair for Point B is (0, 6).

 

 

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 (6, 7)?

Possible Answers:

Point E

Point A

Point B

Point D

Point C

Correct answer:

Point C

Explanation:

Start at point (0, 0) in the bottom, left corner of the the coordinate plane. From there, count right 6 spaces. This is the first number in the given ordered pair. From that point, count up 7 spaces. This is the second number in the given ordered pair.

 

By moving right 6 and up 7, you should have found Point C.

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 E

Point C

Point D

Point A

Point B

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.

 

 

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

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (2, 4); Point X (3, 6); Point Y (5, 4); Point Z (6, 6)

 

 

A polygon is formed with vertices W, X, Y, and Z. Which type of polygon is formed? 

Possible Answers:

Trapezoid

Parallelogram

Square

Kite

Pentagon

Correct answer:

Parallelogram

Explanation:

Begin by plotting the points and connecting the vertices.

Screenshot_2015-03-24_at_4.55.16_pm

 

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both squares and parallelograms. Because the figure does not contain right angles and the sides are not all the same length, it must be a parallelogram.

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

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point W (1, 1); Point X (7, 3); Point Y (1, 6); Point Z (7, 8)

A polygon is formed with vertices W, X, Y, and Z. Which type of polygon is formed? 

Possible Answers:

Hexagon

Triangle

Rhombus

Trapezoid

Parallelogram

Correct answer:

Parallelogram

Explanation:

Begin by plotting and connecting the vertices.

Screenshot_2015-03-24_at_5.02.50_pm

 

The quadrilateral that is created has two sets of parallel sides. Out of the possible answer choices, this can describe both rhombuses and parallelograms. Because the sides are not all the same length, it must be a parallelogram.

Example Question #11 : Coordinate Geometry

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point X (7, 0); Point Y (7, 5); Point Z (0, 5)

 

A polygon is formed with vertices X, Y, and Z. Which type of polygon is formed? 

Possible Answers:

Triangle

Rectangle

Parallelogram

Pentagon

Square

Correct answer:

Triangle

Explanation:

Start by graphing and connecting the vertices.

Screenshot_2015-03-24_at_5.31.16_pm

 

The created figure has 3 sides and 3 angles. The only answer choice that has these characteristics is the triangle.

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

A coordinate plane is shown.

Blank_grid

Ralph plotted the following points on the coordinate grid:

Point X (8, 8); Point Y (1, 4); Point Z (6, 5)

A polygon is formed with vertices X, Y, and Z. Which type of polygon is formed? 

 

 
Possible Answers:

Rectangle

Quadrilateral

Triangle

Square

Correct answer:

Triangle

Explanation:

Start by plotting and connecting the ordered pairs.

Screenshot_2015-03-24_at_5.35.48_pm

 

The created figure has 3 sides and 3 angles. The only answer choice that has these characteristics is the triangle.

 

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

Which of the following sets of points would form a triangle if plotted on a coordinate plane?

Possible Answers:

Correct answer:

Explanation:

A triangle consist of three points.  The correct answer is the only set that contains three points. 

Example Question #1 : How To Find The Perimeter Of A Parallelogram

Untitled_11

What is the perimeter of parallelogram ABCD?

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

The perimeter of a parallelogram is very easy to find. You just need to add up all the sides. However, you need to notice that the sides "across" from each other are equal on parallelograms. So, your figure could be redrawn:

Untitled_11

The perimeter of your figure is therefore:

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