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GED Math : GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #23 : Midpoint Formula

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

(89,58)

(40,38)

(55,89)

(59,85)

Correct answer:

(59,85)

Explanation:

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

To find the midpoint, we will use midpoint formula, which essentially averages out the x and y values of our points.

Midpoint formula:

$(x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Now, plug in our points and solve!

$(x_m,y_m)=(\frac{19+99}{2}, \frac{47+123}{2})=(\frac{118}{2},\frac{170}{2})=(59,85)$

So, we have our answer:

(59,85)

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Example Question #24 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (-7, 5) and (10, -2) .

Possible Answers:

$(\frac{3}{2}, \frac{3}{2})$

$(\frac{2}{3}, \frac{3}{2})$

$(\frac{17}{2}, \frac{3}{2})$

$(\frac{15}{2}, \frac{17}{2})$

Correct answer:

$(\frac{3}{2}, \frac{3}{2})$

Explanation:

Recall how to find the midpoint of a line:

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Plug in the given points to find the midpoint.

$\text{Midpoint}=(\frac{-7+10}{2}, \frac{5+(-2)}{2})=(\frac{3}{2}, \frac{3}{2})$

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Example Question #1801 : Ged Math

Use the distance formula to calculate the distance between the points $\small \small (4,2)$ and $\small (-7,3)$ .

Possible Answers:

$\small 2\sqrt2$

$\small \sqrt{10}$

$\small \sqrt{34}$

$\small \sqrt{122}$

Correct answer:

$\small \sqrt{122}$

Explanation:

The distance between 2 points can be determined using the distance formula:

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

$\small D=\sqrt{(4-(-7))^2+(2-3)^2}$

$\small D=\sqrt{(11)^2+(-1)^2}$

$\small D=\sqrt{121+1}=\sqrt{122}$

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Example Question #1802 : Ged Math

Provide your answer in its most simplified form.

Find the distance between the following two points: (7,0), (-3,5)

Possible Answers:

$\sqrt{113}$

$\sqrt{153}$

$\sqrt{125}$

$\sqrt{51}$

$5\sqrt{5}$

Correct answer:

$5\sqrt{5}$

Explanation:

To find the distance we need to use the distance formula:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values to get:

$d = \sqrt{(7 - (-3))^{2} + (0 - 5)^{2}}$

Combine like terms to get:

$d = \sqrt{(10)^{2} + (-5)^{2}}$

Continue with your order of operations:

$d = \sqrt{100 + 25}$

$d = \sqrt{125}$

Don't forget to simplify if possible:

$d = 5\sqrt{5}$

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Example Question #3 : Distance Formula

Provide your answer in its most simplified form.

Find the distance between these two points: (-10,-4), (3,8)

Possible Answers:

$\sqrt{313}$

$\sqrt{-313}$

$\sqrt{65}$

$\sqrt{193}$

$\sqrt{33}$

Correct answer:

$\sqrt{313}$

Explanation:

For this problem we must use the distance formula:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values:

$d = \sqrt{((-10) - 3)^{2} + ((-4) - 8)^{2}}$

Combine like terms:

$d = \sqrt{(-13)^{2} + (-12)^{2}}$

Continue your order of operations:

$d = \sqrt{169 +144}$

$d = \sqrt{313}$

This cannot be simplified so you are left with the correct answer.

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Example Question #4 : Distance Formula

Provide your answer in its most simplified form.

Find the distance between the two following points: (2,2). (5,6)

Possible Answers:

$\sqrt{55}$

$\sqrt{137}$

$\sqrt{25}$

Correct answer:

Explanation:

We must use the distance formula to solve this problem:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values:

$d = \sqrt{(2 - 5)^{2} + (2 - 6)^{2}}$

Combine like terms:

$d = \sqrt{(-3)^{2} + (-4)^{2}}$

Continue with your order of operations

$d = \sqrt{9 + 16}$

$d = \sqrt{25}$

Simplify to get:

d = 5

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Example Question #841 : Geometry And Graphs

What is the distance between the points (3,2) and (-5,6) ?

Possible Answers:

$4\sqrt{5}$

$5\sqrt{2}$

$16\sqrt5$

$2\sqrt5$

$5\sqrt{3}$

Correct answer:

$4\sqrt{5}$

Explanation:

Write the distance formula.

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

Substitute the points into the formula.

$D=\sqrt{(-5-3)^2+(6-2)^2}$

$D=\sqrt{(-8)^2+(4)^2} = \sqrt{64+16} = \sqrt{80}$

Factor the radical using factors of perfect squares.

$\sqrt{80} = \sqrt{16}\cdot \sqrt5$

The answer is: $4\sqrt{5}$

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Example Question #2 : Distance Formula

Find the distance from point (3,1) to (-1,8) .

Possible Answers:

$\sqrt{53}$

$\sqrt{83}$

$\sqrt{65}$

$5\sqrt{13}$

$3\sqrt5$

Correct answer:

$\sqrt{65}$

Explanation:

Write the formula to find the distance between two points.

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

Substitute the points into the radical.

$D = \sqrt{(-1-3)^2+(8-1)^2}$

$D = \sqrt{(-4)^2+(7)^2} = \sqrt{16+49} = \sqrt{65}$

The answer is: $\sqrt{65}$

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Example Question #2 : Distance Formula

What is the distance between (-2,3) and (5,1) ?

Possible Answers:

$9\sqrt{7}$

$\sqrt{51}$

$\sqrt{53}$

$3\sqrt5$

Correct answer:

$\sqrt{53}$

Explanation:

Write the distance formula.

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

Substitute the points into the equation.

$D = \sqrt{(5-(-2))^2+(1-3)^2} = \sqrt{7^2 + (-2)^2} = \sqrt{49+4}$

The answer is: $\sqrt{53}$

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Example Question #841 : Geometry And Graphs

Use distance formula to find the distance between the following two points.

(43,54) (22,76)

Possible Answers:

$5\sqrt{37}$

$5\sqrt{39}$

$37\sqrt{5}$

925

Correct answer:

$5\sqrt{37}$

Explanation:

Use distance formula to find the distance between the following two points.

(43,54) (22,76)

Distance formula is as follows:

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

Note that it doesn't matter which point is "1" and which point is "2" just so long as we remain consistent.

So, let's plug and chug.

$d=\sqrt{(43-22)^2+(54-76)^2}=\sqrt{21^2+(-22)^2}=\sqrt{441+484}=\sqrt{925}$

$d=\sqrt{925}=\sqrt{25}\sqrt{37}=5\sqrt{37}$

So, our answer is

$5\sqrt{37}$

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All GED Math Resources

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #23 : Midpoint Formula

Example Question #24 : Midpoint Formula

Example Question #1801 : Ged Math

Example Question #1802 : Ged Math

Example Question #3 : Distance Formula

Example Question #4 : Distance Formula

Example Question #841 : Geometry And Graphs

Example Question #2 : Distance Formula

Example Question #2 : Distance Formula

Example Question #841 : Geometry And Graphs

All GED Math Resources

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