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

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Question

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

Answer

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.

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Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

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