Answer:
Explanation:
Given points P(4, 2) and Q(13, 14), you want the length of PQ and its midpoint.
(a) Length
The length of PQ is given by the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
d = ((13 -4)² +(14 -2)²) = √(9² +12²) = √225
d = 15
The length of PQ is 15 units.
(b) Midpoint
The midpoint is halfway between the end points. It is conveniently found as the average of the coordinates of the end points.
M = (P +Q)/2
M = ((4, 2) +(13, 14))/2 = (4+13, 2+14)/2 = (17, 16)/2
M = (8.5, 8)
The midpoint of PQ is M(8.5, 8).
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Additional comment
The length of PQ is the hypotenuse of a right triangle with side lengths 9 and 12 units. You recognize this ratio as 3:4, so the triangle is a 3-4-5 right triangle, scaled up by a factor of 3. The length PQ is 3·5 = 15.
{3, 4, 5} is one of several Pythagorean triples commonly seen in textbook problems. Others include {5, 12, 13}, {7, 24, 25}, {8, 15, 17}.
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