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GED Math : Geometry and Graphs

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Example Questions

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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Example Question #3 : Distance Formula

A triangle on a coordinate plane has the following vertices: (5, 5), (10, 2), (8, -2) . What is the perimeter of the triangle?

Possible Answers:

17.92

18.04

14.53

23.10

Correct answer:

17.92

Explanation:

Since we are asked to find the perimeter of the triangle, we will need to use the distance formula to find the length of each side. Recall the distance formula:

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

Start by finding the distance between the points $(5, 5)\text{ and }(10, 2)$ :

$\text{Distance}=\sqrt{(2-5)^2+(10-5)^2}=\sqrt{9+25}=\sqrt{34}$

Next, find the distance between $(10, 2)\text{ and }(8, -2)$ .

$\text{Distance}=\sqrt{(-2-2)^2+(8-10)^2}=\sqrt{16+4}=\sqrt{20}$

Then, find the distance between $(5, 5)\text{ and }(8, -2)$ .

$\text{Distance}=\sqrt{(-2-5)^2+(8-5)^2}=\sqrt{49+9}=\sqrt{58}$

Finally, add up the lengths of each side to find the perimeter of the triangle.

$\text{Perimeter}=\sqrt{54}+\sqrt{20}+\sqrt{58}=17.92$

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Example Question #4 : Distance Formula

Find the distance between the points and .

Possible Answers:

144

407

202

404

Correct answer:

407

Explanation:

Find the distance between the points and .

To find the distance between two points, we will use distance formula (clever name). Distance formula can be thought of as a modified Pythagorean Theorem. What distance formula does is essentially treats our two points as the ends of a hypotenuse on a right triangle, then uses the two side lengths to find the hypotenuse.

Distance formula:

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

Pythagorean Theorem

c^2=a^2+b^2

If the connection isn't clear, don't worry, we can still solve for distance.

$D=\sqrt{(413-9)^2+(65-17)^2}$

$D=\sqrt{(404)^2+(48)^2}$

$D=\sqrt{165520}$

$D=406.84\approx 407$

So our answer is 407

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Example Question #11 : Distance Formula

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

Possible Answers:

$\sqrt{181}$

$\sqrt{146}$

$6\sqrt{3}$

$12\sqrt{2}$

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 #12 : Distance Formula

Find the length of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

145

150

110

330

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:

$10\sqrt{7}$

$25\sqrt{3}$

$3\sqrt{5}$

$5\sqrt{13}$

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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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

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

Example Question #3 : Distance Formula

Example Question #4 : Distance Formula

Example Question #11 : Distance Formula

Example Question #12 : Distance Formula

Example Question #11 : Distance Formula

All GED Math Resources

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