+912 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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+2440 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. |
| \(\text{MDPT}_{\overline{PR}}\left(\frac{-2}{2},\frac{-1}{2}\right)\) | |
| \(\text{MDPT}_{\overline{PR}}\left(-1,\frac{-1}{2}\right)\) | |
| \(\text{MDPT}_{\overline{PR}}\left(-1,-0.5\right)\) |
+2440 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. |
| \(\text{MDPT}_{\overline{PR}}\left(\frac{-2}{2},\frac{-1}{2}\right)\) | |
| \(\text{MDPT}_{\overline{PR}}\left(-1,\frac{-1}{2}\right)\) | |
| \(\text{MDPT}_{\overline{PR}}\left(-1,-0.5\right)\) |
