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

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

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All ISEE Lower Level Quantitative Resources

20 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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

Vt_custom_xy_xytriangle_1

Find the area of the above triangle--given that it has a base of and a height of .

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of the right triangle apply the formula: $A=\frac{base\times height}{2}$

Thus, the solution is:

$A=\frac{6\times 8}{2}=\frac{48}{2}=24$

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

Vt_custom_xy_xytriangle2

The above triangle has a base of and a height of . Find the area.

Possible Answers:

square units

Correct answer:

square units

Explanation:

To find the area of this right triangle apply the formula: $A=\frac{base \times height}{2}$

Thus, the solution is:

$A=\frac{12\times 6}{2}=\frac{72}{2}=36$

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

Vt_custom_xy_xytriangle2

The above triangle has a base of and a height of . Find the length longest side (the hypotenuse).

Possible Answers:

144

180

$\sqrt{144}$

$\sqrt{180}$

Correct answer:

$\sqrt{180}$

Explanation:

In order to find the length of the longest side of the triangle (hypotenuse), apply the formula:

a^2 +b^2=c^2 , where and are equal to and , respectively. And, the hypotenuse.

Thus, the solution is:

6^2 +12^2=c^2
36+144=c^2
180=c^2
$c=\sqrt{180}$

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Example Question #4 : How To Find A Triangle On A Coordinate Plane

Vt_custom_xy_xytriangle3

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

Possible Answers:

104 square units

square units

Correct answer:

square units

Explanation:

To find the area of this triangle apply the formula: $A=\frac{base\times height}{2}$

Thus, the solution is:

$A=\frac{13\times 8}{2}=\frac{104}{2}=52$

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Example Question #5 : How To Find A Triangle On A Coordinate Plane

Vt_custom_xy_xytriangle3

At which of the following coordinate points does this triangle intersect with the -axis?

Possible Answers:

(0,-7)

(-7,0)

(-8,0)

(0,7)

Correct answer:

(0,-7)

Explanation:

This triangle only intersects with the vertical -axis at one coordinate point: (0,-7) . Keep in mind that the represents the value of the coordinate and represents the value of the coordinate point.

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

Vt_custom_xy_xytriangle3

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

Possible Answers:

$21+\sqrt{33}$

$21+\sqrt{233}$

$\sqrt{233}$

Correct answer:

$21+\sqrt{233}$

Explanation:

The perimeter of this triangle can be found using the formula: $P=height + base +\sqrt{height^2 +base^2}$

Thus, the solution is:

$P=13+8+\sqrt{8^2+13^2}$
$P=21 +\sqrt{64+169}$
$P=21+\sqrt{233}$

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

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the area of the triangle.

Possible Answers:

square units

Correct answer:

square units

Explanation:

In order to find the area of this triangle apply the formula: $A=\frac{base \times height}{2}= \frac{4\times 3}{2}=\frac{12}{2}=6$

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

Vt_custom_xy_xytriangle3

The triangle shown above has a base of and height of . Find the length of the longest side of the triangle (the hypotenuse).

Possible Answers:

$\sqrt{169}$

233

169

$\sqrt{64}$

$\sqrt{233}$

Correct answer:

$\sqrt{233}$

Explanation:

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

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the hypotenuse (the longest side).

Possible Answers:

Correct answer:

Explanation:

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

Vt_custom_xy_xytriangle_4

The above triangle has a height of and a base with length . Find the perimeter of the triangle.

Possible Answers:

Correct answer:

Explanation:

The perimeter of this triangle can be found using the formula: $P=height + base +\sqrt{height^2 +base^2}$

Thus, the solution is:

$P=3+4+\sqrt{3^2+4^2}$
$P=7+\sqrt{9+16}$
$P=7+\sqrt{25}$
P=7+5=12

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : How to find a triangle 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 Triangle On A Coordinate Plane

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

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

Example Question #4 : How To Find A Triangle On A Coordinate Plane

Example Question #5 : How To Find A Triangle On A Coordinate Plane

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

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

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

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

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

All ISEE Lower Level Quantitative Resources

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