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ISEE Lower Level Quantitative : How to find a parallelogram on a coordinate plane

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All ISEE Lower Level Quantitative Resources

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Example Questions

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

New_vt_custom_xy_plane5

The parallelogram shown above has a height of and a base of length . Find the area of the parallelogram.

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of the parallelogram apply the formula: $A=base\times height$

Since, the paralleogram has a base of and a height of the solution is:
$A=5\times4=20$

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

New_vt_custom_xy_plane5

The parallelogram shown above has a height of and a base of length . Find the perimeter of the parallelogram.

Possible Answers:

$P=2(\sqrt{20}+4)$

$P=2(\sqrt{20}+5)$

$P=(\sqrt{20}+5)$

p=2(20+5)

Correct answer:

$P=2(\sqrt{20}+5)$

Explanation:

In order to find the correct perimeter of the parallelogram apply the formula: P=2(a+b) , where the length of one of the diagonal sides and the length of the base.

In order to find the length of side , apply the formula: a^2+b^2=C^2 . By drawing an altitude from point (4,4) to (4,0) , a right triangle is formed with a base that has a length of and a height of .

Thus, the solution is:
a^2 +b^2=c^2
2^2+4^2= length of side a^2
4+16=20
a^2=20
$a=\sqrt{20}$

Therefore,

$P=2(\sqrt{20}+b)$
b=5
$P=2(\sqrt{20}+5)$

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

New_vt_custom_xy_plane6

Identify the coordinate points for the parallelogram that is shown above.

Possible Answers:

(-2,1), (-1,2), (-3,-2), (-2,-1)

(2,-2),(1,2),(3,2),(2,-1)

(-2,-2),(1,2),(3,2),(2,-1)

(-2,-1), (-1,2), (3,2), (2,-1)

Correct answer:

(-2,-1), (-1,2), (3,2), (2,-1)

Explanation:

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.

Thus, the parallelogram has coordinate points: (-2,-1), (-1,2), (3,2), (2,-1)

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

New_vt_custom_xy_plane6

What is the area of the parallelogram shown above?

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of the parallelogram that is shown, apply the formula: $A=base\times height$
Since the parallelogram has a base of and a height of the solution is:
$A=4\times 3=12$

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Example Question #5 : Geometry

New_vt_custom_xy_plane6

Given that the above parallelogram has base sides with a length of and diagonal sides with a length of $\sqrt{10}$ what is the perimeter of the parallelogram?

Possible Answers:

P=2(10+4)

$P=2(\sqrt{10}-4)$

$P=2(\sqrt{10}+4)$

$P=(\sqrt{10}+4)$

$P=2(\sqrt{10}+3)$

Correct answer:

$P=2(\sqrt{10}+4)$

Explanation:

In order to find the perimeter of the parallelogram apply the formula: P=2(a+b) , where the length of one diagonal side and the length of one base.

In this problem, $a=\sqrt{10}$ and b= 4 .
Thus, the correct answer is: $P=2(\sqrt{10}+4)$

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

New_vt_custom_xy_plane5

Identify the coordinate points for the parallelogram shown above.

Possible Answers:

(2,1), (4,4), (7,0), (9,-4)

(2,0), (4,4), (7,0), (9,4)

(2,5), (4,0), (7,1), (9,3)

(-2,0), (4,4), (7,3), (9,4)

Correct answer:

(2,0), (4,4), (7,0), (9,4)

Explanation:

In order to identify the coordinate points for this parallelogram, notice that there must be two different pairs of coordinates with the same values.

Thus, the correct set of coordinates is:
(2,0), (4,4), (7,0), (9,4)

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : How to find a parallelogram on a coordinate plane

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

All ISEE Lower Level Quantitative Resources

Example Questions

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

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

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

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

Example Question #5 : Geometry

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

All ISEE Lower Level Quantitative Resources

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