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Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

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All Common Core: High School - Geometry Resources

6 Diagnostic Tests 114 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #341 : High School: Geometry

In slope intercept form, find the equation of the line parallel to y = 10 x + 13 and goes through the point $\left ( 7, \quad 8\right )$ .

Possible Answers:

y = 10 x - 52

y = 10 x - 62

y = 10 x - 72

$y = - \frac{x}{10} + \frac{187}{10}$

$y = - \frac{x}{10} + \frac{87}{10}$

Correct answer:

y = 10 x - 62

Explanation:

First step is to recall slope intercept form.

$y - y_{0} = m{\left (x - x_{0} \right )}$

Where is the slope, and $\left(x_0,y_0\right)$ is a point on the line.

Since we want a line that is parallel, our slope () is going to be the same as the original equation.

So m = 10

Then we substitute 7 for $x_{0}$ and 8 for $y_{0}$

After plugging them in, we get.

y - 8 = 10 x - 70

Now we solve for

y = 10 x - 62

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Example Question #62 : Expressing Geometric Properties With Equations

In slope intercept form, find the equation of the line parallel to y = 11 x + 2 and goes through the point $\left ( -4, \quad -6\right )$ .

Possible Answers:

$y = - \frac{x}{11} + \frac{40}{11}$

y = 11 x + 38

y = 11 x + 28

y = 11 x + 48

$y = - \frac{x}{11} - \frac{70}{11}$

Correct answer:

y = 11 x + 38

Explanation:

First step is to recall slope intercept form.

$y - y_{0} = m{\left (x - x_{0} \right )}$

Where is the slope, and $\left(x_0,y_0\right)$ is a point on the line.

Since we want a line that is parallel, our slope () is going to be the same as the original equation.

So m = 11

Then we substitute -4 for $x_{0}$ and -6 for $y_{0}$

After plugging them in, we get.

y + 6 = 11 x + 44

Now we solve for

y = 11 x + 38

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Example Question #1 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Find the midpoint of a line segment with endpoints of (10, 12) and (-4, -13).

Possible Answers:

$\left ( 6, \quad -1\right )$

$\left ( 7.0, \quad 12.5\right )$

$\left ( -14, \quad -25\right )$

$\left ( -2.5, \quad -0.9230769230769231\right )$

$\left ( 3.0, \quad -0.5\right )$

Correct answer:

$\left ( 3.0, \quad -0.5\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for .

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = 3, \quad y_{m} = - \frac{1}{2}\right )$

To verify the result, plot the points on a graph.

Plot7

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Example Question #1 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Find the midpoint of a line segment with endpoints of (10, 12) and (-4, -13).

Possible Answers:

$\left ( 7.0, \quad 12.5\right )$

$\left ( -14, \quad -25\right )$

$\left ( -2.5, \quad -0.9230769230769231\right )$

$\left ( 3.0, \quad -0.5\right )$

$\left ( 6, \quad -1\right )$

Correct answer:

$\left ( 3.0, \quad -0.5\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for .

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = 3, \quad y_{m} = - \frac{1}{2}\right )$

To verify the result, plot the points on a graph.

Plot7

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Example Question #61 : Expressing Geometric Properties With Equations

Find the midpoint of a line segment with endpoints of (7, 1) and (2, 5) .

Possible Answers:

$\left ( 3.5, 0.2\right )$

$\left ( -5, 4\right )$

$\left ( 4.5, 3.0\right )$

$\left ( 9, 6\right )$

$\left ( 2.5, -2.0\right )$

Correct answer:

$\left ( 4.5, 3.0\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for .

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = \frac{9}{2}, \quad y_{m} = 3\right )$

Plot the end points and the midpoint to verify the result.

Plot1

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Example Question #62 : Expressing Geometric Properties With Equations

Find the midpoint of a line segment with endpoints of (-9, 10) and (-16, -17) .

Possible Answers:

$\left ( 3.5, \quad 13.5\right )$

$\left ( -12.5, \quad -3.5\right )$

$\left ( -7, \quad -27\right )$

$\left ( -25, \quad -7\right )$

$\left ( 0.5625, \quad -0.5882352941176471\right )$

Correct answer:

$\left ( -12.5, \quad -3.5\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_{1}}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{25}{2}, \quad y_{m} = - \frac{7}{2}\right )$
Plot the points to verify the result.

Plot2

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Example Question #5 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Find the midpoint of a line segment with endpoints of (-9, -11) and (3, 4) .

Possible Answers:

$\left ( -3.0, \quad -2.75\right )$

$\left ( -6.0, \quad -7.5\right )$

$\left ( 12, \quad 15\right )$

$\left ( -6, \quad -7\right )$

$\left ( -3.0, \quad -3.5\right )$

Correct answer:

$\left ( -3.0, \quad -3.5\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_{1}}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = -3, \quad y_{m} = - \frac{7}{2}\right )$

Plot the points to verify the result.

Plot3

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Example Question #63 : Expressing Geometric Properties With Equations

Find the midpoint of a line segment with endpoints of (-2, -15) and (-8, -13) .

Possible Answers:

$\left ( 3.0, \quad -1.0\right )$

$\left ( 0.25, \quad 1.1538461538461537\right )$

$\left ( -5.0, \quad -14.0\right )$

$\left ( -10, \quad -28\right )$

$\left ( -6, \quad 2\right )$

Correct answer:

$\left ( -5.0, \quad -14.0\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for .

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = -5, \quad y_{m} = -14\right )$

Now, plot the points to verify the results.

Plot5

Report an Error

Example Question #64 : Expressing Geometric Properties With Equations

Find the midpoint of a line segment with endpoints of (5, 3) and (-16, -1) .

Possible Answers:

$\left ( -21, \quad -4\right )$

$\left ( -0.3125, \quad -3.0\right )$

$\left ( -11, \quad 2\right )$

$\left ( 10.5, \quad 2.0\right )$

$\left ( -5.5, \quad 1.0\right )$

Correct answer:

$\left ( -5.5, \quad 1.0\right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{11}{2}, \quad y_{m} = 1\right )$

Now, plot the points to verify the results.

Plot6

Report an Error

Example Question #8 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Find the midpoint of a line segment with endpoints of (-8, 4) and (3, -14) .

Possible Answers:

$\left ( 7.0, \quad 12.5\right )$

$\left ( -14, \quad -25\right )$

$\left( -2.5, \quad -5.0 \right )$

$\left ( -2.5, \quad -0.9230769230769231\right )$

$\left ( 6, \quad -1\right )$

Correct answer:

$\left( -2.5, \quad -5.0 \right )$

Explanation:

In order to find the midpoint between these end points, we need to recall the midpoint formula.

$\left ( x_{m} = \frac{x_{0}}{2} + \frac{x_{1}}{2}, \quad y_{m} = \frac{y_{0}}{2}+\frac{y_1}{2}\right )$

Where $x_{m}$ is the mid point for and $y_{m}$ is the midpoint for .

Now we simply substitute values for $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{5}{2}, \quad y_{m} = -5\right )$

To verify the result, plot the points on a graph.

Plot8

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Common Core: High School - Geometry : Expressing Geometric Properties with Equations

Study concepts, example questions & explanations for Common Core: High School - Geometry

All Common Core: High School - Geometry Resources

Example Questions

Example Question #341 : High School: Geometry

Example Question #62 : Expressing Geometric Properties With Equations

Example Question #1 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #1 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #61 : Expressing Geometric Properties With Equations

Example Question #62 : Expressing Geometric Properties With Equations

Example Question #5 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #63 : Expressing Geometric Properties With Equations

Example Question #64 : Expressing Geometric Properties With Equations

Example Question #8 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

All Common Core: High School - Geometry Resources

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