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GRE Subject Test: Math : Coordinate Geometry

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Example Questions

Example Question #21 : Distance & Midpoint Formulas

Given two points, (1,7) and (6,11) , find the midpoint.

Possible Answers:

(9,-3.5)

(-3.5,9)

(9,3.5)

(3.5,9)

Correct answer:

(3.5,9)

Explanation:

Step 1: Define midpoint. The midpoint is a point located between two given points.. If I draw a line through these points, I get a straight line

Step 2: The midpoint formula is: $\bigg(\frac {x_1+x_2}{2},\frac {y_1+y_2}{2}\bigg)$

Step 3. Plug in the values:

$\bigg(\frac {1+6}{2},\frac {7+11}{2}\bigg)$

Step 4: Simplify each fraction in Step 3:

$\bigg(\frac {7}{2},\frac {18}{2}\bigg)$

Step 5: Convert each fraction to a decimal from step 4:

(3.5,9)

The midpoint is (3.5,9)

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Example Question #32 : Calculus

Find the length of the line that connects the points: (4,7) and (8,15) .

Possible Answers:

$-4\sqrt{10}$

$4\sqrt{157}$

$4\sqrt{5}$

$\sqrt{586}$

Correct answer:

$4\sqrt{5}$

Explanation:

Step 1: Recall the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step 2: Find x_1, x_2, y_1, y_2 ...

x_1=4, x_2=8, y_1=7, y_2=15

Step 3: Substitute the values into the equation:

$d=\sqrt{(8-4)^2+(15-7)^2}$
Reduce the parentheses:

$d=\sqrt{4^2+8^2}$
Evaluate the exponents and add:

$d=\sqrt{16+64}=\sqrt{80}$

Step 4: Reduce $\sqrt{80}$ into lowest terms...

$\sqrt{80}=\sqrt{4}\cdot \sqrt{4}\cdot \sqrt 5$

Using rule of square roots, multiplying two roots with the same value on the inside just gives me the inside value..

$\sqrt{80}=[\sqrt{4}\cdot \sqrt{4}]\cdot \sqrt{5}$
$\sqrt{80}=4\sqrt{5}$

The length of the line that connects both points is $4\sqrt{5}$ .

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Example Question #22 : Distance & Midpoint Formulas

What is the distance between (4,6) and (11,7)

Possible Answers:

$5\sqrt{2}$

$2\sqrt{5}$

$5\sqrt{3}$

Correct answer:

$5\sqrt{2}$

Explanation:

Step 1: Plug in values into the distance formula:

$\sqrt{({11-4})^2+(7-6)^2}$

Step 2: Evaluate the inside...

$\sqrt{7^2+1^2}=\sqrt{50}$

Step 3: Simplify...

$\sqrt{50}=\sqrt{25}\sqrt{2}=5\sqrt2$

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Example Question #32 : Functions And Graphs

Find the midpoint between (5,-2) and (9,-4)

Possible Answers:

(7,-3)

(-2, -1)

(3,3/2)

(3,-6)

(3,3)

Correct answer:

(7,-3)

Explanation:

To find the midpoint you must use the equation

$\left (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$ Insert numbers

$\left (\frac{5+9}{2}, \frac{-2+-4}{2} \right )$

(7,-3)

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Example Question #22 : Distance & Midpoint Formulas

Find the distance between the two points

(3,-4), (2,5)

Possible Answers:

$\sqrt{82}$

$\sqrt{58}$

$\sqrt{93}$

Correct answer:

$\sqrt{82}$

Explanation:

You must use the distance formula

$\sqrt{({x}_{2}+{x}_{1})^{2}+({y}_{2}+{y}_{1})^{2}}$ Fill in with the points

$\sqrt{({2}+{3})^{2}+({5}+{-4})^{2}}}$ Solve

$\sqrt{({-1})^{2}+({9})^{2}}$

$\sqrt{{1}+{81}}$

$\sqrt{82}$

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Example Question #1 : Slope & Intercept

What is the slope and y-intercept of this line: 3x-4y=12 ?

Possible Answers:

$Slope=\frac {3}{4},y-intercept=3$

$Slope=\frac {4}{3},y-intercept=3$

$Slope=\frac {-3}{4},y-intercept=3$

$Slope=\frac {3}{4},y-intercept=2$

Correct answer:

$Slope=\frac {3}{4},y-intercept=3$

Explanation:

Step 1: Move the y-term to the other side. We will add 4y.

3x-4y+(4y)=12+(4y)
$\rightarrow 3x=12+4y$

Step 2: Move the constant to the other side. We will subtract 12.

3x+(-12)=12+(-12)+4y
$\rightarrow 3x-12=4y$

Step 3: Divide by the coefficient in front of the y term. In this question, we divide all terms by 4.

$\frac {3x-12}{4}=\frac {4y}{4}\rightarrow\frac {3}{4}x+\frac {-12}{4}=y$

$\rightarrow y=\frac {3}{4}x-3$

Step 4: Identify the slope and the y-intercept. The slope is the number that is in front of the x term, and the y-intercept is the number that comes after the x-term.

In this question, the slope is $\frac {3}{4}$ and the y-intercept is .

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Example Question #1 : Slope & Intercept

Find the slope of a line that passes through points Y(-5,-1) and Z(3,-1) .

Possible Answers:

m = 8

m=0

Slope is undefined.

m=-8

Correct answer:

m=0

Explanation:

The formula for slope is:

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

$m = \frac{-1 -(-1)}{3-(-5)}$

$m=\frac{0}{8}$

m=0

When the y coordinates are the same, as in this case both were -1, this would form a horizontal line. The slope of a horizontal line is zero.

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Example Question #1 : Slope & Intercept

Find the slope of a line that passes through points X(4,2) and Y (4,1).

Possible Answers:

Slope is undefined.

m=0

m=-3

m=3

Correct answer:

Slope is undefined.

Explanation:

The formula for slope is:

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

$m = \frac{-1-2}{4-4}$

$m= \frac{-3}{0}$

Slope is undefined.

If the x coordinates are the same, as in this problem both x coordinates are 4, then this will be a vertical line. The slope of a vertical line is undefined.

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Example Question #2 : Slope & Intercept

Find the slope of a line that passes through points Q (-1,-3) and R (1,2).

Possible Answers:

$m=\frac{1}{2}$

m=0

Slope is undefined.

$m=\frac{5}{2}$

Correct answer:

$m=\frac{5}{2}$

Explanation:

The formula for slope is:

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

$m = \frac{2-(-3)}{1-(-1)}$

$m = \frac{5}{2}$

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Example Question #45 : Functions And Graphs

What is the slope and y-intercept of the following equation?

x+y =4

Possible Answers:

m=-4 and b = -1

m = -1 and b = 4

m=1 and b =1

m= 4 and b = -1

Correct answer:

m = -1 and b = 4

Explanation:

x + y = 4

Subtract from both sides of the equation.

y = 4-x

Write equation in the form of y=mx +b .

y = -1x +4

m= -1

b = 4 ( represents the y-intercept)

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GRE Subject Test: Math : Coordinate Geometry

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #21 : Distance & Midpoint Formulas

Example Question #32 : Calculus

Example Question #22 : Distance & Midpoint Formulas

Example Question #32 : Functions And Graphs

Example Question #22 : Distance & Midpoint Formulas

Example Question #1 : Slope & Intercept

Example Question #1 : Slope & Intercept

Example Question #1 : Slope & Intercept

Example Question #2 : Slope & Intercept

Example Question #45 : Functions And Graphs

All GRE Subject Test: Math Resources

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