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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 : Coordinate Geometry

Find the coordinate of the midpoint of the line segment connecting the pair of points

(0, 0) and (8, 0) .

Possible Answers:

Cannot be determined

(0, 4))

(4, 0)

(-4, 0)

Correct answer:

(4, 0)

Explanation:

The coordinate of the midpoint of the line segment connecting a pair of points is

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ .

So for the pair of points (x_1,y_1)=(0, 0) and (x_2,y_2)=(8, 0)

we get,

$\left(\frac{0+8}{2}, \frac{0+0}{2}\right)=(4, 0)$

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Example Question #1 : Midpoint Formula

A line extends from the origin to $\small (14, -2)$ . What is its midpoint?

Possible Answers:

$\small (7,-1)$

$\small (1,-7)$

$\small (28, -4)$

$\small (7, 1 )$

$\small (-7, -1)$

Correct answer:

$\small (7,-1)$

Explanation:

The origin is the point $\small (0,0)$ . We can use the regular midpoint formula with $\small (0,0)$ as $\small (x_{1}, y_{1})$ and the given point $\small (14, -2)$ as $\small (x_{2}, y_{2})$ :

$\small (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

$\small (\frac{0+14}{2} , \frac{0+-2}{2})$

$\small (\frac{14}{2}, \frac{-2}{2}) = (7, -1)$

Note that since the first point is the origin, we're averaging these points with 0, or in other words just dividing by 2.

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Example Question #8 : Midpoint Formula

There is a line segment between the two points (5, 10) and (3, 6). What formula will give you the correct mid-point of the line segment?

Possible Answers:

$\Big( {5-2} \; ,{10-2} \Big )$

$\Big( \frac{5+10}{2} \; , \frac{3+6}{2} \Big )$

$\Big( \frac{5-3}{2} \; , \frac{10-6}{2} \Big )$

$\Big( \frac{5-10}{2} \; , \frac{3-6}{2} \Big )$

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

Correct answer:

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

Explanation:

To find the mid-point given two points on the coordinate plane you are basically finding the average of the x-values and the average of the y-values. To do this follow the formula below:

$\Big( \frac{x_{1}+ x_{2}}{2} \; , \frac{y_{1}+y_{2}}{2} \Big )$

With our points this gives:

$\Big( \frac{5+3}{2} \; , \frac{10+6}{2} \Big )$

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Example Question #7 : Midpoint Formula

A line has endpoints at (4,5) and (-6,8). Where is its midpoint?

Possible Answers:

$\left(\frac{13}{2},-1\right)$

$\left(1,\frac{13}{2}\right)$

$\left(\frac{-13}{2},-1\right)$

$\left(\frac{-13}{2},1\right)$

$\left(-1,\frac{13}{2}\right)$

Correct answer:

$\left(-1,\frac{13}{2}\right)$

Explanation:

The midpoint is the point that is equidistant from each endpoint point.

We find it using a formula that computes the average of the x and y coordinates.

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

$\left(\frac{4+(-6)}{2},\frac{5+8}{2}\right)$

$\left(\frac{-2}{2},\frac{13}{2}\right)$

$\mathbf{\left(-1,\frac{13}{2}\right)}$

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Example Question #1 : Midpoint Formula

A line segment has the endpoints (2, 4) and (1, 8) . What is the midpoint of this line segment?

Possible Answers:

$(\frac{3}{2},6)$

$(\frac{1}{2},12)$

(6, 3)

$(\frac{5}{2},2)$

Correct answer:

$(\frac{3}{2},6)$

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{2+1}{2}, \frac{4+8}{2})=(\frac{3}{2}, 6)$

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Example Question #11 : Coordinate Geometry

A line segment has endpoints (8, 1) and (2, 5). What is the midpoint of this segment?

Possible Answers:

(3, 12)

(5, 1)

$(\frac{13}{2}, \frac{1}{2})$

(5, 3)

Correct answer:

(5, 3)

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{8+2}{2}, \frac{1+5}{2})=(5, 3)$

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Example Question #12 : Coordinate Geometry

A line segment has endpoints at (10, 2) and (-10, -6). What is the midpoint of this line?

Possible Answers:

(0, -2)

(-2, 2)

(8, 1)

(0, -4)

Correct answer:

(0, -2)

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-10}{2}, \frac{2-6}{2})=(0, -2)$

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Example Question #13 : Coordinate Geometry

A line segments has endpoints at (-5, 1) and (-2, 9). What is the midpoint of this line segment?

Possible Answers:

$(-\frac{5}{2}, 4)$

(3, 1)

$(-\frac{7}{2}, 5)$

$(\frac{9}{2}, 2)$

Correct answer:

$(-\frac{7}{2}, 5)$

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-5-2}{2}, \frac{1+9}{2})=(-\frac{7}{2}, 5)$

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Example Question #14 : Coordinate Geometry

Find the midpoint of a line that has endpoints at (9, 2) and (11, 6).

Possible Answers:

(15, 13)

(20, 8)

(10, 4)

(13, 2)

Correct answer:

(10, 4)

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{9+11}{2}, \frac{2+6}{2})=(10, 4)$

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Example Question #15 : Coordinate Geometry

Find the midpoint of a line that has endpoints at (-15, 2) and (-2, 2).

Possible Answers:

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

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

$(-\frac{13}{2},2)$

(-12, 2)

Correct answer:

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

Explanation:

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{-15-2}{2}, \frac{2+2}{2})=(-\frac{17}{2}, 2)$

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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 : Coordinate Geometry

Example Question #1 : Midpoint Formula

Example Question #8 : Midpoint Formula

Example Question #7 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #11 : Coordinate Geometry

Example Question #12 : Coordinate Geometry

Example Question #13 : Coordinate Geometry

Example Question #14 : Coordinate Geometry

Example Question #15 : Coordinate Geometry

All Intermediate Geometry Resources

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