Question
For the point P(10,3) and Q(17,8), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ. What is the distance?
For the point P(10,3) and Q(17,8), find the distance d(P,Q) and the coordinates of the midpoint M of the segment PQ. What is the distance?
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Koala Tutor
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To find the distance between the points P(10,3) and Q(17,8), we can use the distance formula:
d(P,Q) = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates of P(10,3) and Q(17,8):
d(P,Q) = √((17 - 10)^2 + (8 - 3)^2)
= √(7^2 + 5^2)
= √(49 + 25)
= √74
Therefore, the distance d(P,Q) is √74.
To find the coordinates of the midpoint M, we can use the midpoint formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Using the coordinates of P(10,3) and Q(17,8):
M = ((10 + 17)/2, (3 + 8)/2)
= (27/2, 11/2)
Therefore, the coordinates of the midpoint M are (27/2, 11/2).
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