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GED Math : Coordinate Geometry

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Example Questions

Example Question #833 : Geometry And Graphs

The two endpoints of a line segment are (1,4) and (5,10) . Find the midpoint of the line segment.

Possible Answers:

(5,5)

(7,3)

(1,4)

(3,7)

(4,6)

Correct answer:

(3,7)

Explanation:

To find the midpoint of a line, you basically have to average the two values and average the two values. In other words, you have to add the two values and then divide by , and add the two values and then divide by . The standard equation for the midpoint formula is $((x_{1} + x_{2}) / 2, (y_{1} + y_{2}) / 2)$ .

The two values are and , and (1+5)/2=3 , so the coordinate of your midpoint is . The two values are and , and (4+10)/2 = 7 , so the coordinate of your midpoint is .

Therefore, the midpoint is (3,7) .

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Example Question #21 : Midpoint Formula

Find the midpoint of the line connecting and .

Possible Answers:

(222,42)

(211,41)

(202,41)

(202,24)

Correct answer:

(211,41)

Explanation:

Find the midpoint of the line connecting and .

To find the midpoint, we will essentially average out our x and y values independently.

What this will look like is:

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

So, all we need to do is find the average of each of our dimensions and we are set.

$(x_m,y_m)=(\frac{9+413}{2},\frac{17+65}{2})=(\frac{422}{2},\frac{82}{2})=(211,41)$

So, our answer is:

(211,41)

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Example Question #21 : Midpoint Formula

A line with endpoints (1, 4) and (a, b) has a midpoint at (5, 12) . What is the value of a+b ?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the midpoint of a segment:

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

Solve for :

$\frac{a+1}{2}=5$

a+1=10

a=9

Solve for :

$\frac{b+4}{2}=12$

b+4=24

b=20

Thus, a+b=9+20=29

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Example Question #121 : Coordinate Geometry

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

(59,85)

(55,89)

(40,38)

(89,58)

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 #23 : Midpoint Formula

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

Possible Answers:

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

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

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

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

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 #1 : Distance Formula

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

Possible Answers:

$\small 2\sqrt2$

$\small \sqrt{10}$

$\small \sqrt{122}$

$\small \sqrt{34}$

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 #2 : Distance Formula

Provide your answer in its most simplified form.

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

Possible Answers:

$\sqrt{153}$

$\sqrt{113}$

$\sqrt{51}$

$\sqrt{125}$

$5\sqrt{5}$

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:

$\sqrt{313}$

$\sqrt{193}$

$\sqrt{-313}$

$\sqrt{65}$

$\sqrt{33}$

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:

$\sqrt{137}$

$\sqrt{25}$

$\sqrt{55}$

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 #2 : Distance Formula

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

Possible Answers:

$5\sqrt{2}$

$5\sqrt{3}$

$4\sqrt{5}$

$2\sqrt5$

$16\sqrt5$

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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GED Math : Coordinate Geometry

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #833 : Geometry And Graphs

Example Question #21 : Midpoint Formula

Example Question #21 : Midpoint Formula

Example Question #121 : Coordinate Geometry

Example Question #23 : Midpoint Formula

Example Question #1 : Distance Formula

Example Question #2 : Distance Formula

Example Question #3 : Distance Formula

Example Question #4 : Distance Formula

Example Question #2 : Distance Formula

All GED Math Resources

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