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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find The Endpoints Of A Line Segment

What is the midpoint between the two points:

(0,0) and (3,4)

Possible Answers:

(2,1.5)

(3,4)

(4,3)

(1.5,2)

(9,16)

Correct answer:

(1.5,2)

Explanation:

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

If we plug in our points we get

$\left(\frac{0+3}{2},\frac{0+4}{2}\right)$

$\left(\frac{3}{2},\frac{4}{2}\right)$

(1.5,2)

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Example Question #21 : Lines

What is the midpoint between the two points:

(1,9) and (3, 5)

Possible Answers:

(2,5)

(2,7)

(7,2)

(1,9)

(3,4)

Correct answer:

(2,7)

Explanation:

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

So lets plug in our two points, that gives us

$\left(\frac{1+3}{2},\frac{9+5}{2}\right)$

$\left(\frac{4}{2},\frac{14}{2}\right)$

(2,7)

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Example Question #4 : How To Find The Endpoints Of A Line Segment

What is the midpoint between the two points:

(0,0) and (4,5)

Possible Answers:

(2,2.5)

(2,5)

(4,2.5)

(4,5)

(2,2)

Correct answer:

(2,2.5)

Explanation:

The equation to find the midpoint between two points is

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

If we plug in our values of the two points we get

$\left(\frac{0+4}{2},\frac{0+5}{2}\right)$

$\left(\frac{4}{2},\frac{5}{2}\right)$

(2,2.5)

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Example Question #5 : How To Find The Endpoints Of A Line Segment

One of the endpoints of a line is $\small (8, -7)$ and the midpoint is $\small (1, -3)$ . What is the other endpoint?

Possible Answers:

$\small (15, 1 )$

$\small (-6, 1)$

$\small (-6, -11)$

$\small (15, -11)$

$\small (3, -1)$

Correct answer:

$\small (-6, 1)$

Explanation:

The midpoint's coordinates are the average of the endpoints'.

This means that the x-coordinates of the two endpoints have a mean of 1:

$\small \frac{8+x }{2} = 1$ multiply both sides by 2

$\small 8 + x = 2$ subtract 8

$\small x = -6$ this means the other endpoint's x-coordinate is -6

This also means that the y-coordinates of the two endpoints have a mean of -3:

$\small \frac{-7+y}{2} = -3$ multiply both sides by 2

$\small -7 + y = -6$ add 7 to both sides

$\small y = 1$

The coordinate pair that we're looking for is (-6, 1)

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Example Question #22 : Lines

The midpoint of a line is $\small (9, 9)$ and one of the endpoints is $\small (1, 17)$ . What is the other endpoint?

Possible Answers:

$\small (8, -8)$

$\small (-7, 1 )$

$\small (17, 25)$

$\small (-7, 25)$

$\small (17, 1)$

Correct answer:

$\small (17, 1)$

Explanation:

The midpoint's coordinates are just the mean of the endpoints'.

This means that the mean of the two x-coordinates is 9:

$\small \frac{x+ 1}{2} = 9$ multiply both sides by 2

$\small x + 1 = 18$ subtract 1

$\small x = 17$

This also means that the mean of the two y-coordinates is 9:

$\small \frac{y+17}{2} = 9$ multiply both sides by 2

$\small y + 17 = 18$ subtract 17

$\small y = 1$

So the other endpoint we were solving for is $\small (17, 1 )$

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Example Question #7 : How To Find The Endpoints Of A Line Segment

The midpoint for a line with an endpoint at (3, 1) is (7, 8) . What are the coordinates for the other endpoint?

Possible Answers:

(11, 15)

(2, 6)

(15, 11)

(-1, -7)

Correct answer:

(11, 15)

Explanation:

Recall how to find the midpoint of a line:

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

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{3+x}{2}=7$

3+x=14

x=11

Now, let's solve for the coordinate.

$\frac{y+1}{2}=8$

y+1=16

y=15

The coordinate for the other endpoint must be (11, 15) .

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Example Question #1 : How To Find The Endpoints Of A Line Segment

A line with the endpoints (5, 1) and (a, b) has a midpoint at (-10, 2) . What are the coordinates for the unknown endpoint?

Possible Answers:

(2, -10)

(-25, 3)

(-15, 4)

(-15, -3)

Correct answer:

(-25, 3)

Explanation:

Recall how to find the midpoint of a line:

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

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{5+a}{2}=-10$

5+a=-20

a=-25

Now, let's solve for the coordinate.

$\frac{b+1}{2}=2$

b+1=4

b=3

The coordinate for the other endpoint must be (-25, 3) .

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Example Question #2 : How To Find The Endpoints Of A Line Segment

A line with endpoints at (-9, -2) and (c, d) has a midpoint of (5, -9) . What are the coordinates for the unknown endpoint?

Possible Answers:

(19, -16)

(-20, -15)

(15, 12)

(-14, -2)

Correct answer:

(19, -16)

Explanation:

Recall how to find the midpoint of a line:

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

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-9+c}{2}=5$

-9+c=10

c=19

Now, let's solve for the coordinate.

$\frac{-2+d}{2}=-9$

-2+d=-18

d=-16

The coordinate for the other endpoint must be (19, -16) .

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Example Question #1 : How To Find The Endpoints Of A Line Segment

A line with endpoints at (-1, -2) and (e, f) has a midpoint of (8, 8) . What are the coordinates of the unknown endpoint?

Possible Answers:

(16, 17)

(18, 19)

(17, 18)

(15, 16)

Correct answer:

(17, 18)

Explanation:

Recall how to find the midpoint of a line:

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

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-1+e}{2}=8$

-1+e=16

e=17

Now, let's solve for the coordinate.

$\frac{-2+f}{2}=8$

-2+f=16

f=18

The coordinate for the other endpoint must be (17, 18) .

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Example Question #33 : Lines

A line with endpoints (6, -1) and (g, h) has a midpoint of (7, 2) . What are the coordinates of the unknown endpoint?

Possible Answers:

(8, 1)

(2, 7)

(8, 5)

(6, 7)

Correct answer:

(8, 5)

Explanation:

Recall how to find the midpoint of a line:

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

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{6+g}{2}=7$

6+g=14

g=8

Now, let's solve for the coordinate.

$\frac{-1+h}{2}=2$

-1+h=4

h=5

The coordinate for the other endpoint must be (8,5) .

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #21 : Lines

Example Question #4 : How To Find The Endpoints Of A Line Segment

Example Question #5 : How To Find The Endpoints Of A Line Segment

Example Question #22 : Lines

Example Question #7 : How To Find The Endpoints Of A Line Segment

Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #2 : How To Find The Endpoints Of A Line Segment

Example Question #1 : How To Find The Endpoints Of A Line Segment

Example Question #33 : Lines

All Intermediate Geometry Resources

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