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What are the endpoint coordinates for the midsegment of △PQR that is parallel to PQ¯¯¯¯¯?

Enter your answer, as a decimal or whole number, in the boxes.

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AngelRay  Nov 4, 2017

Best Answer 

 #1
avatar+1375 
+3

A midsegment is a segment joining the midpoint of two sides of a triangle. Each triangle has 3 midsegments. The Triangle Midsegment Theorem states that a midsegment of a triangle is parallel to the nonintersecting side, and its length is half the length of the nonintersecting side.  

 

 

In this diagram here, \(\overline{BD}\), the midsegment, bisects both of its intersected sides. Also, \(\overline{BD}\parallel\overline{AE}\) and \(\frac{1}{2}\text{AE}=\text{BD}\)

 

Knowing this information, we can then determine where the coordinates of the endpoints of the midsegment will be.

 

Let's find the midpoint of both of the segments. 

 

\(\text{MDPT}_{\overline{PR}}\left(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}\right)\)Find the midpoint of the segment PR using this formula.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-3-4}{2},\frac{3-2}{2}\right)\)Simplify from here to find the midpoint.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-7}{2},\frac{1}{2}\right)\)Since the answers must be in decimal format, I will convert them.
\(\text{MDPT}_{\overline{PR}}\left(-3.5,0.5\right)\) 

 

Now, find the other midpoint.

 

\(\text{MDPT}_{\overline{QR}}\left(\frac{2-4}{2},\frac{1-2}{2}\right)\)Simplify from here.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-2}{2},\frac{-1}{2}\right)\) 
\(\text{MDPT}_{\overline{PR}}\left(-1,\frac{-1}{2}\right)\) 
\(\text{MDPT}_{\overline{PR}}\left(-1,-0.5\right)\) 
TheXSquaredFactor  Nov 5, 2017
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1+0 Answers

 #1
avatar+1375 
+3
Best Answer

A midsegment is a segment joining the midpoint of two sides of a triangle. Each triangle has 3 midsegments. The Triangle Midsegment Theorem states that a midsegment of a triangle is parallel to the nonintersecting side, and its length is half the length of the nonintersecting side.  

 

 

In this diagram here, \(\overline{BD}\), the midsegment, bisects both of its intersected sides. Also, \(\overline{BD}\parallel\overline{AE}\) and \(\frac{1}{2}\text{AE}=\text{BD}\)

 

Knowing this information, we can then determine where the coordinates of the endpoints of the midsegment will be.

 

Let's find the midpoint of both of the segments. 

 

\(\text{MDPT}_{\overline{PR}}\left(\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}\right)\)Find the midpoint of the segment PR using this formula.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-3-4}{2},\frac{3-2}{2}\right)\)Simplify from here to find the midpoint.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-7}{2},\frac{1}{2}\right)\)Since the answers must be in decimal format, I will convert them.
\(\text{MDPT}_{\overline{PR}}\left(-3.5,0.5\right)\) 

 

Now, find the other midpoint.

 

\(\text{MDPT}_{\overline{QR}}\left(\frac{2-4}{2},\frac{1-2}{2}\right)\)Simplify from here.
\(\text{MDPT}_{\overline{PR}}\left(\frac{-2}{2},\frac{-1}{2}\right)\) 
\(\text{MDPT}_{\overline{PR}}\left(-1,\frac{-1}{2}\right)\) 
\(\text{MDPT}_{\overline{PR}}\left(-1,-0.5\right)\) 
TheXSquaredFactor  Nov 5, 2017

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