GMAT Math : Geometry

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Example Questions

Example Question #21 : How To Graph An Ordered Pair

Which quadrants can include the point (AB, A + B) if nonzero numbers and have the same sign?

Possible Answers:

Either Quadrant I or Quadrant II

Either Quadrant II or Quadrant III

Either Quadrant I or Quadrant III

Either Quadrant I or Quadrant IV

Either Quadrant II or Quadrant IV

Correct answer:

Either Quadrant I or Quadrant IV

Explanation:

If and have the same sign, then AB > 0 , and the point has a positive -coordinate. The sign of A + B is the same as the common sign of and . Therefore, only the -coordinate restricts the possibilities.

The points witn positive -coordinates are in Quadrant I and Quadrant IV.

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Example Question #191 : Advanced Geometry

Which quadrant or axis can include the point (4,3) ?

Possible Answers:

Quadrant I

Quadrant II

Quadrant IV

Quadrant III

The -axis

Correct answer:

Quadrant I

Explanation:

The ordered pair (4,3) consists of a positive -coordinate and a positive -coordinate. The only quadrant that consists entirely of positive - and -coordinates is Quadrant I.

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Example Question #3 : Graphing An Ordered Pair

Which quadrant or axis contains the point (5,0) ?

Possible Answers:

Quadrant II

The -axis

Quadrant I

The -axis

Quadrant III

Correct answer:

The -axis

Explanation:

The ordered pair (5,0) consists of a positive -coordinate and a -coordinate of . The only part of the coordinate plane on which all points have a zero -coordinate is the -axis.

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Example Question #791 : Geometry

Which of the following ordered pairs is in Quadrant III?

Possible Answers:

(5,2)

(-5,0)

(-5,2)

(5,-2)

(-5,-2)

Correct answer:

(-5,-2)

Explanation:

By definition, only Quadrant III contains ordered pairs that have both negative - and -coordinates.

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Example Question #2 : Graphing An Ordered Pair

Which quadrant or axis includes the point (-1,3) ?

Possible Answers:

The -axis

Quadrant IV

Quadrant I

Quadrant III

Quadrant II

Correct answer:

Quadrant II

Explanation:

The ordered pair (-1,3) has a negative -coordinate and a positive -coordinate. By definition, all ordered pairs with negative -coordinates and a positive -coordinates exist in Quadrant II.

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Example Question #108 : Graphing

Which quadrant or axis includes the point (0,7) ?

Possible Answers:

Quadrant III

The -axis

Quadrant I

Quadrant II

Correct answer:

The -axis

Explanation:

The ordered pair (0,7) has a zero -coordinate and a nonzero -coordinate. By definition, all ordered pairs with zero -coordinates and nonzero -coordinates is on the -axis.

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Example Question #3 : Graphing An Ordered Pair

Which of the following ordered pairs is in Quadrant I?

Possible Answers:

(2,7)

(2,-7)

(-2,7)

None of these coordinates

(-2,-7)

Correct answer:

(2,7)

Explanation:

By definition, all ordered pairs with positive -coordinates and positive -coordinates are in Quadrant I. Therefore, the only ordered pair in this quadrant is (2,7) .

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Example Question #792 : Geometry

The point (3,k) lies on a line with slope m=-2 that passes through the point (2,5) .

What is ?

Possible Answers:

cannot be determined

Correct answer:

Explanation:

We first need to find an equation of the line with a slope of that passes through the point (2, 5).

y-5=-2(x-2)

y-5=-2x+4

y=-2x+9

Now, plug in the point (3,k) and solve for .

k=-2(3)+9=3

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Example Question #793 : Geometry

A line goes through points (4, 8), (1, 4), (-3, N) . What is ?

Possible Answers:

$N=-3 \frac{1}{3}$

N = -1

N = -7

$N=-1 \frac{1}{3}$

$N=-9 \frac{1}{3}$

Correct answer:

$N=-1 \frac{1}{3}$

Explanation:

The slope of the line through (4, 8) and (1, 4) can be found using the slope formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Set $x_{1}=1,x_{2} = 4, y_{1}=4,y_{2} = 8$ :

$m = \frac{8-4}{4-1} = \frac{4}{3}$

We can use this slope and the slope formula; set $x_{1}=1,x_{2} = -3, y_{1}=4,y_{2} = N$ :

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}} = m$

$\frac{N-4}{-3-1} = \frac{4}{3}$

$\frac{N-4}{-4} = \frac{4}{3}$

$\frac{N-4}{-4}\cdot \left ( -4\right ) = \frac{4}{3} \cdot \left ( -4\right )$

$N-4= -\frac{16}{3}$

$N-4+4= -\frac{16}{3} +4$

$N= -\frac{4}{3} = -1 \frac{1}{3}$

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Example Question #3 : Graphing A Point

The point (5,v) lies on a line with a slope m=3 that passes through (1,2) . What is the value of ?

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

In order to find the value of , we first need to find the equation for the line with slope m=3 that passes through the point (1,2) .

y-2=3(x-1)

y-2=3x-3

y=3x-1

Plugging in (5,v) and solving for :

v=3(5)-1

v=15-1

v=14

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GMAT Math : Geometry

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #21 : How To Graph An Ordered Pair

Example Question #191 : Advanced Geometry

Example Question #3 : Graphing An Ordered Pair

Example Question #791 : Geometry

Example Question #2 : Graphing An Ordered Pair

Example Question #108 : Graphing

Example Question #3 : Graphing An Ordered Pair

Example Question #792 : Geometry

Example Question #793 : Geometry

Example Question #3 : Graphing A Point

All GMAT Math Resources

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