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

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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.

(  ,  ) and (  ,  ) Nov 4, 2017

### Best Answer

#1
+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. $$\text{MDPT}_{\overline{PR}}\left(\frac{-2}{2},\frac{-1}{2}\right)$$ $$\text{MDPT}_{\overline{PR}}\left(-1,\frac{-1}{2}\right)$$ $$\text{MDPT}_{\overline{PR}}\left(-1,-0.5\right)$$
Nov 5, 2017

### 1+0 Answers

#1
+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