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GED Math : Distance Formula

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Example Questions

Example Question #11 : Distance Formula

What is the distance between the points (5, 1) and (-5, 10) ?

Possible Answers:

$12\sqrt{2}$

$\sqrt{181}$

$6\sqrt{3}$

$\sqrt{146}$

Correct answer:

$\sqrt{181}$

Explanation:

Recall the distance formula:

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

Plug in the given points to find the distance between them.

$\text{Distance}=\sqrt{(5-(-5))^2+(1-10)^2}=\sqrt{100+81}=\sqrt{181}$

The distance between those points is $\sqrt{181}$ .

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Example Question #131 : Coordinate Geometry

Find the length of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

150

330

145

110

Correct answer:

110

Explanation:

Find the length of the line connecting the following points.

(19,47) (99,123)

To find the length of a line, use distance formula.

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

What we are really doing is making a right triangle and using Pythagorean Theorem to find the hypotenuse.

Let's plug in our points and find the distance!

$d=\sqrt{(123-47)^2+(99-19)^2}$

$d=\sqrt{(76)^2+(80)^2}$

$d=\sqrt{(5776+6400}=\sqrt{12176}$

$\sqrt{12176}\approx 110$

So our answer is 110

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Example Question #11 : Distance Formula

What is the distance between the points (4,5) and (22,6) ?

Possible Answers:

$10\sqrt{7}$

$3\sqrt{5}$

$25\sqrt{3}$

$5\sqrt{13}$

Correct answer:

$5\sqrt{13}$

Explanation:

Remember that you can consider your two points as:

(x_1,y_1) and (x_2,y_2)

From this, remember that the distance formula is:

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

Now, for your data, this is:

$\sqrt{(22-4)^2+(6-5)^2}$

$\sqrt{(18)^2+(1)^2}=\sqrt{324+1}=\sqrt{325}$

You can simplify this value a little. Identify the prime factors of 325 and move any number that appears in a pair of factors from the interior to the exterior of the square root symbol:

$\sqrt{5\cdot5\cdot13}=5\sqrt{13}$

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Example Question #12 : Distance Formula

What is the distance between the two points (-10,15) and (-11,-20) ?

Possible Answers:

$19\sqrt{13}$

$15\sqrt{22}$

$\sqrt{2283}$

$55\sqrt{19}$

$\sqrt{1226}$

Correct answer:

$\sqrt{1226}$

Explanation:

Remember that you can consider your two points as:

(x_1,y_1) and (x_2,y_2)

From this, remember that the distance formula is:

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

Now, for your data, this will look like the following. Be very careful with the negative signs:

$\sqrt{(-11-(-10))^2+(-20-15)^2}$

$\sqrt{(-1)^2+(-35)^2}=\sqrt{1+1225}=\sqrt{1226}$

1226 is only factorable into and 613 ; therefore, your answer is in its final form already.

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GED Math : Distance Formula

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Distance Formula

Example Question #131 : Coordinate Geometry

Example Question #11 : Distance Formula

Example Question #12 : Distance Formula

All GED Math Resources

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