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GED Math : Coordinate Geometry

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Example Questions

Example Question #5 : Distance Formula

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

Possible Answers:

$\sqrt{83}$

$3\sqrt5$

$\sqrt{53}$

$\sqrt{65}$

$5\sqrt{13}$

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 #5 : Distance Formula

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

Possible Answers:

$\sqrt{51}$

$\sqrt{53}$

$9\sqrt{7}$

$3\sqrt5$

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 #2 : Distance Formula

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

(43,54) (22,76)

Possible Answers:

$37\sqrt{5}$

$5\sqrt{37}$

$5\sqrt{39}$

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 #841 : Geometry And Graphs

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:

23.10

17.92

18.04

14.53

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 #3 : Distance Formula

Find the distance between the points and .

Possible Answers:

407

404

202

144

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:

$12\sqrt{2}$

$\sqrt{181}$

$6\sqrt{3}$

$\sqrt{146}$

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 #132 : Coordinate Geometry

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

Possible Answers:

$25\sqrt{3}$

$3\sqrt{5}$

$5\sqrt{13}$

$10\sqrt{7}$

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 #133 : Coordinate Geometry

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

Possible Answers:

$19\sqrt{13}$

$\sqrt{1226}$

$\sqrt{2283}$

$55\sqrt{19}$

$15\sqrt{22}$

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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Example Question #134 : Coordinate Geometry

A line has slope $\frac{3}{4}$ and -intercept (0, -7) . Give its -intercept.

Possible Answers:

$\left (5\frac{1}{4}, 0 \right )$

$\left (-5\frac{1}{4}, 0 \right )$

$\left (- 9 \frac{1}{3}, 0 \right )$

$\left ( 9 \frac{1}{3}, 0 \right )$

Correct answer:

$\left ( 9 \frac{1}{3}, 0 \right )$

Explanation:

The -intercept will be a point (a,0) for some value . We use the slope formula

$\frac{y_{2}- y _{1}}{x_{2}- x _{1}} = m$ ,

setting $m = \frac{3}{4}, x_{1} =0, x_{2} = a, y_{1} = -7, y_{2} =0$ ,

and solving for :

$\frac{0- (-7)}{a-0} = \frac{3}{4}$

$\frac{ 7}{a} = \frac{3}{4}$

$\frac{ 7}{a} \cdot a = \frac{3}{4} \cdot a$

$7= \frac{3}{4} \cdot a$

$\frac{4} {3}\cdot 7= \frac{4} {3}\cdot \frac{3}{4} \cdot a$

$a = \frac{28} {3} = 9 \frac{1}{3}$

The -intercept is $\left ( 9 \frac{1}{3}, 0 \right )$ .

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GED Math : Coordinate Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #5 : Distance Formula

Example Question #5 : Distance Formula

Example Question #2 : Distance Formula

Example Question #841 : Geometry And Graphs

Example Question #3 : Distance Formula

Example Question #11 : Distance Formula

Example Question #131 : Coordinate Geometry

Example Question #132 : Coordinate Geometry

Example Question #133 : Coordinate Geometry

Example Question #134 : Coordinate Geometry

All GED Math Resources

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