Geometry - 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).

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

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

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

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

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

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

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

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

From here, plot the points to verify the result.

Plot12

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

Find the midpoint of a line segment with endpoints of and .

$\left ( -13.5, \quad -3.0\right )$

$\left ( -27, \quad -6\right )$

$\left ( 0.5, \quad -0.25\right )$

$\left ( -9, \quad -10\right )$

$\left ( 4.5, \quad 5.0\right )$

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

$\left ( x_{m} = - \frac{27}{2}, \quad y_{m} = -3\right )$

Now, plot the points to verify the result.

Plot9

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

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

Now plot the points to verify the results.

Plot7

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

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

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

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

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

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

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

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

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

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

Plot8

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

Find the midpoint of a line segment with endpoints of and .

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

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

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

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

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

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

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

Now, plot the points to verify the results.

Plot5

Points that Partitions Segments in a Given Ratio: CCSS.Math.Content.HSG-GPE.B.6

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