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Common Core: High School - Geometry : Points that Partitions Segments in a Given Ratio: CCSS.Math.Content.HSG-GPE.B.6

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 #11 : 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 (0, -5) and (-20, -9) .

Possible Answers:

$\left ( -0.0, \quad 0.5555555555555556\right )$

$\left ( 10.0, \quad 2.0\right )$

$\left ( -20, \quad -4\right )$

$\left ( -10.0, \quad -7.0\right )$

$\left ( -20, \quad -14\right )$

Correct answer:

$\left ( -10.0, \quad -7.0\right )$

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 $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = -10, \quad y_{m} = -7\right )$

Now plot the points to verify the result.

Plot10

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Example Question #12 : 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, 9) and (-10, -4) .

Possible Answers:

$\left ( -19, \quad -13\right )$

$\left ( -0.9, \quad -2.25\right )$

$\left ( -1, \quad 5\right )$

$\left ( 9.5, \quad 6.5\right )$

$\left ( -0.5, \quad 2.5\right )$

Correct answer:

$\left ( -0.5, \quad 2.5\right )$

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 $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{1}{2}, \quad y_{m} = \frac{5}{2}\right )$

From here, plot the points to verify the midpoint.

Plot11

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Example Question #13 : 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 (13, -9) and (-14, -14) .

Possible Answers:

$\left ( -1, \quad -23\right )$

$\left ( 13.5, \quad 2.5\right )$

$\left ( -0.9285714285714286, \quad 0.6428571428571429\right )$

$\left ( -0.5, \quad -11.5\right )$

$\left ( -27, \quad -5\right )$

Correct answer:

$\left ( -0.5, \quad -11.5\right )$

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 $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{1}{2}, \quad y_{m} = - \frac{23}{2}\right )$

From here, plot the points to verify the result.

Plot12

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Example Question #14 : 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, 5) and (-7, 3) .

Possible Answers:

$\left ( 1.1428571428571428, \quad 1.6666666666666667\right )$

$\left ( -7.5, \quad 4.0\right )$

$\left ( 1, \quad -2\right )$

$\left ( -0.5, \quad 1.0\right )$

$\left ( -15, \quad 8\right )$

Correct answer:

$\left ( -7.5, \quad 4.0\right )$

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 $x_{0}$ , $x_{1}$ , $y_{0}$ , $y_{1}$

$\left ( x_{m} = - \frac{15}{2}, \quad y_{m} = 4\right )$

Now, plot the points to verify the results.

Plot4

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All Common Core: High School - Geometry Resources

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Common Core: High School - Geometry : Points that Partitions Segments in a Given Ratio: CCSS.Math.Content.HSG-GPE.B.6

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

All Common Core: High School - Geometry Resources

Example Questions

Example Question #11 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #12 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #13 : Points That Partitions Segments In A Given Ratio: Ccss.Math.Content.Hsg Gpe.B.6

Example Question #14 : 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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