+0  
 
0
909
1
avatar+1015 

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.

(  ,  ) and (  ,  )

 

AngelRay  Nov 4, 2017

Best Answer 

 #1
avatar+2248 
+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
 #1
avatar+2248 
+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

30 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.