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ISEE Lower Level Quantitative : Coordinate Geometry

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

Example Question #141 : Geometry

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:

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:

3^2+4^2=c^2
9+16=c^2
c^2=25
$c=\sqrt{25}=5$

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Example Question #142 : Geometry

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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Example Question #143 : Geometry

Vt_custom_xy_xytriangle_5

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

Possible Answers:

square units

10.5 square units

square units

17.5 square units

square units

Correct answer:

17.5 square units

Explanation:

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

Thus, the solution is:

$A=\frac{7\times 5}{2}=\frac{35}{2}=17.5$

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Example Question #144 : Geometry

Vt_custom_xy_xytriangle_1

Given that this triangle has a base of and a height of , what is the length of the longest side?

Possible Answers:

120

$\sqrt{36}$

Correct answer:

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 +8^2=c^2
36 +64=100
c^2= 100
$c=\sqrt{100}$

c=10

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Example Question #142 : Geometry

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 Line On A Coordinate Plane

Vt_custom_xy_xylinesegment1

Which equation of a line is parallel to line segment $\bar{AB}$ ?

Possible Answers:

$y=-\frac{9}{13}-6$

$y=\frac{9}{13}-8$

$y=\frac{13}{9}+5$

$y=\frac{5}{12}+4$

Correct answer:

$y=\frac{9}{13}-8$

Explanation:

In order for the equation to represent a line that is parallel to the line that is shown, the equation must have the same slope as line segment $\bar{AB}$ .

Since, line segment $\bar{AB}$ has a slope of $\frac{9}{13}$ , the correct equation is: $y=\frac{9}{13}-8$

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

Vt_custom_xy_xysegment_3

The points in the above line segment are apart of which of the following linear equations?

Possible Answers:

x=-7

x=7

y=7

y=-7

Correct answer:

y=-7

Explanation:

The above line segment is a horizontal line that passes through the axis at -7. Since this line is horizontal, it does not have a slope. Therefore, y=-7 is the correct answer.

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Example Question #3 : How To Find A Line On A Coordinate Plane

Vt_custom_xy_xysegment_3

Which of the following linear equations is perpendicular to the line segment shown above?

Possible Answers:

$y=-\frac{1}{2}-7$

y=7

x=-3

y=-7

Correct answer:

x=-3

Explanation:

Since the line segment is horizontal, the equation that is perpendicular to the segment must run vertically. The only linear equation that runs vertically (perpendicular to y=-7 ) is x=-3 .

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

Vt_custom_xy_xysegment_3

At what coordinate point does the line x=-3 intersect with the line segment shown above?

Possible Answers:

(3,7)

(-7,-3)

(3,-7)

(-3,-7)

Correct answer:

(-3,-7)

Explanation:

Since, x=-3 is perpendicular to y=-7 the points must cross at (-3,-7) , because it is the only coordinate point that both lines pass through.

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

Vt_custom_xy_xyline5

At which coordinate point does this line segment cross the -axis?

Possible Answers:

(0,-2)

(0,3)

(-3,0)

(3,0)

Correct answer:

(3,0)

Explanation:

Keep in mind that the values in the coordinate points are (x,y) , thus the point (3,0) is the point at which the line segment passes through the axis.

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All ISEE Lower Level Quantitative Resources

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ISEE Lower Level Quantitative : Coordinate Geometry

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

All ISEE Lower Level Quantitative Resources

Example Questions

Example Question #141 : Geometry

Example Question #142 : Geometry

Example Question #143 : Geometry

Example Question #144 : Geometry

Example Question #142 : Geometry

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

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

Example Question #3 : How To Find A Line On A Coordinate Plane

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

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

All ISEE Lower Level Quantitative Resources

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