Question

Points P, Q and R are collinear such that PQ : QR=2:3 point P is located at (1,3) and point R is located at (11,15)

Answer 1

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:

$Q - P = \frac{2}{5}(R - P)$

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:

$Q - P = \frac{2}{5}(R - P)$

$x - 1 = \frac{2}{5}(11 - 1)$

$x - 1 = \frac{2}{5}10$

$x - 1 = 4$

$x = 5$

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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:

$Q - P = \frac{2}{5}(R - P)$

$y - 3 = \frac{2}{5}(15 - 3)$

$y - 3 = \frac{24}{5}$

$y - 3 = 4.8$

$y = 7.8$

The coordinates of Q are (5,7.8).

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• The midpoint of segment PQ is the mean of the coordinates, thus:

$M = (\frac{1 + 11}{2}, \frac{3 + 15}{2}) = (\frac{12}{2}, \frac{18}{2}) = (6,9)$

The midpoint of segment PQ is M(6,9).

A similar problem is given at brainly.com/question/24148182