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Colt1911 [192]
3 years ago
10

What are the coordinates of the endpoints of the midsegment for △XYZ that is parallel to XZ⎯⎯⎯⎯⎯ ?

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
7 0

The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)

Step-by-step explanation:

In a triangle the segment which joining the mid points of two sides:

  • Parallel to the 3rd side
  • Its length is equal half the length of the 3rd side
  • It's called the mid-segment of the triangle

In Δ XYZ

∵ Vertex X is (0 , 7)

∵ Vertex Y is (2 , 5)

∵ Vertex Z is (0 , 1)

∵ The mid-segment of Δ XYZ is parallel to XZ

- The mid-segment intersects the other two sides of the Δ

  at their mid-points

∴ The mid-segment intersects XY and YZ at their midpoints

∴ The endpoints of the mid-segment are the midpoints of

   XY and YZ

The mid point of a segments whose endpoints are (x_{1},y_{1}) and (x_{2},y_{2}) is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

∵ X = (0 , 7) and Y = (2 , 5)

∴ x_{1} = 0 and x_{2} = 2

∴ y_{1} = 7 and y_{2} = 5

∵ The mid point of XY = (\frac{0+2}{2},\frac{7+5}{2})

∴ The mid point of XY = (\frac{2}{2},\frac{12}{2})

∴ The mid point of XY = (1 , 6)

∵ Z = (0 , 1) and Y = (2 , 5)

∴ x_{1} = 0 and x_{2} = 2

∴ y_{1} = 1 and y_{2} = 5

∵ The mid point of ZY = (\frac{0+2}{2},\frac{1+5}{2})

∴ The mid point of ZY = (\frac{2}{2},\frac{6}{2})

∴ The mid point of ZY = (1 , 3)

∵ The endpoints of the mid-segment are the midpoints of

   XY and YZ

∴ The end points of the mid segments are (1 , 6) and (1 , 3)

The coordinates of the endpoints of the mid-segment of Δ XYZ that parallel to XZ are (1 , 6) and (1 , 3)

Learn more:

You can learn more about the mid-point in brainly.com/question/5223123

#LearnwithBrainly

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