GRE Math : Geometry

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Example Questions

Example Question #3 : Coordinate Geometry

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

–3x + 2y = 3

2x – 3y = 5

4x – 5y = 4

–2x + 2y = 3

3x + 5y = 2

Correct answer:

–3x + 2y = 3

Explanation:

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

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Example Question #61 : Lines

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=2x-3$

$\dpi{100} \small y=4x-6$

$\dpi{100} \small y=4x+6$

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=-2x+3$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

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Example Question #1441 : Gre Quantitative Reasoning

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

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Example Question #101 : Algebra

If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?

Possible Answers:

$y=-\frac{1}{8}x+14.375$

$y=\frac{1}{8}x+14.375$

y=-8x+38

$y=-\frac{1}{8}x+13.625$

y=-8x-38

Correct answer:

$y=-\frac{1}{8}x+14.375$

Explanation:

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (–5 –3)

= (1 )/( –8)

=–1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = –3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375

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Example Question #2 : Coordinate Geometry

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=3x+2$

$\dpi{100} \small y=-x+8$

$\dpi{100} \small y=2x-4$

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=x+7$

Correct answer:

$\dpi{100} \small y=-x+8$

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

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Example Question #61 : Geometry

Which of the following equations does NOT represent a line?

Possible Answers:

x=10

x^2+y=10

5y=10

x-y=10

x+y=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

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Example Question #143 : Coordinate Geometry

Let y = 3x – 6.

At what point does the line above intersect the following:

$2x =\frac{2}{3}y+4$

Possible Answers:

They do not intersect

(–5,6)

They intersect at all points

(0,–1)

(–3,–3)

Correct answer:

They intersect at all points

Explanation:

If we rearrange the second equation it is the same as the first equation. They are the same line.

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Example Question #1 : Midpoint Formula

There is a line defined by two end-points, (4,3) and (a,b) . The midpoint between these two points is (7,15) . What is the value of the point (a,b) ?

Possible Answers:

(10,27)

(12,3)

(13,41)

(3,12)

(14,-1)

Correct answer:

(10,27)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{4+a}{2},\frac{3+b}{2}\right)=(7,15)$

You merely need to solve each coordinate for its respective value.

$\frac{4+a}{2}=7$

4+a=14

a=10

Then, for the y-coordinate:

$\frac{3+b}{2}=15$

3+b=30

b=27

Therefore, our other point is: (10,27)

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Example Question #252 : Geometry

There is a line defined by two end-points, (11,-5) and (a,b) . The midpoint between these two points is (-6,-21) . What is the value of the point (a,b) ?

Possible Answers:

(12,-14)

(4,-194)

(5,-26)

(-14,-25)

(-23,-37)

Correct answer:

(-23,-37)

Explanation:

Recall that to find the midpoint of two points (a,b) and (c,d) , you use the equation:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$ .

(It is just like finding the average of the two points, really.)

So, for our equation, we know the following:

$\left(\frac{11+a}{2},\frac{-5+b}{2}\right)=(-6,-21)$

You merely need to solve each coordinate for its respective value.

$\frac{11+a}{2}=-6$

11+a=-12

a=-23

Then, for the y-coordinate:

$\frac{-5+b}{2}=-21$

-5+b=-42

b=-37

Therefore, our other point is: (-23,-37)

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Example Question #1 : Midpoint Formula

What is the other endpoint of a line segment with one point that is (6,8) and a midpoint of (14,1) ?

Possible Answers:

(22,-6)

(7,16)

(12,7)

(-15,-6)

(22,8)

Correct answer:

(22,-6)

Explanation:

Recall that the midpoint formula is like finding the average of the and values for two points. For two points (a,b) and (c,d) , it is:

$\left(\frac{a+c}{2},\frac{b+d}{2}\right)$

For our points, we are looking for (c,d) . We know:

$\left(\frac{6+c}{2},\frac{8+d}{2}\right)=(14,1)$

We can solve for each of these coordinates separately:

X-Coordinate

$\frac{6+c}{2} = 14$

6+c=28

c=22

Y-Coordinate:

$\frac{8+d}{2}=1$

8+d=2

d=-6

Therefore, our point is (22,-6)

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All GRE Math Resources

13 Diagnostic Tests 452 Practice Tests Question of the Day Flashcards Learn by Concept

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GRE Math : Geometry

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #3 : Coordinate Geometry

Example Question #61 : Lines

Example Question #1441 : Gre Quantitative Reasoning

Example Question #101 : Algebra

Example Question #2 : Coordinate Geometry

Example Question #61 : Geometry

Example Question #143 : Coordinate Geometry

Example Question #1 : Midpoint Formula

Example Question #252 : Geometry

Example Question #1 : Midpoint Formula

All GRE Math Resources

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