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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND PLEASE EXPLAIN WHY THAT IS THE ANSWER

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND-example-1

1 Answer

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Answer:

  • PQ = 15
  • M = (8.5, 8)

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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I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS PLEASE AND-example-1
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