Respuesta :
Using line segments, it is found that:
- The coordinates of Q are (5,7.8).
- The midpoint of segment PQ is M(6,9).
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- Point P is located at (1,3).
- Point R is located at (11,15).
- Point Q is located at (x,y).
- PQ:QR = 2:3, which means that:
[tex]Q - P = \frac{2}{5}(R - P)[/tex]
This is used to find the x and y coordinates of Q.
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- The x-coordinate of P is 1.
- The x-coordinate of R is 11.
- The x-coordinate of Q is x.
Thus:
[tex]Q - P = \frac{2}{5}(R - P)[/tex]
[tex]x - 1 = \frac{2}{5}(11 - 1)[/tex]
[tex]x - 1 = \frac{2}{5}10[/tex]
[tex]x - 1 = 4[/tex]
[tex]x = 5[/tex]
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- The y-coordinate of P is 3.
- The y-coordinate of R is 15.
- The y-coordinate of Q is y.
Thus:
[tex]Q - P = \frac{2}{5}(R - P)[/tex]
[tex]y - 3 = \frac{2}{5}(15 - 3)[/tex]
[tex]y - 3 = \frac{24}{5}[/tex]
[tex]y - 3 = 4.8[/tex]
[tex]y = 7.8[/tex]
The coordinates of Q are (5,7.8).
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- The midpoint of segment PQ is the mean of the coordinates, thus:
[tex]M = (\frac{1 + 11}{2}, \frac{3 + 15}{2}) = (\frac{12}{2}, \frac{18}{2}) = (6,9)[/tex]
The midpoint of segment PQ is M(6,9).
A similar problem is given at https://brainly.com/question/24148182
