SAT Exam > SAT Questions > If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) a...
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle then find the length of median through Q.
- a)√24
- b)√38
- c)√11
- d)√53
Correct answer is option 'C'. Can you explain this answer?
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle...
We know, midpoint of (x1, y1, z1) and (x2, y2, z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2).
Midpoint of line PR is (5, 4, 6).
Length of median through Q is distance between midpoint of PR and Q i.e.
Midpoint of line PR is (5, 4, 6).
Length of median through Q is distance between midpoint of PR and Q i.e.
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle...
To find the length of the median through Q, we need to find the midpoint of PR and then calculate the distance between that midpoint and Q.
The midpoint of PR can be found by taking the average of the x-coordinates, the y-coordinates, and the z-coordinates of P and R.
Midpoint of PR = ((2+8)/2, (3+5)/2, (9+3)/2) = (5, 4, 6)
Now, we can calculate the distance between the midpoint of PR and Q using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Distance = sqrt((2-5)^2 + (5-4)^2 + (5-6)^2)
Distance = sqrt((-3)^2 + (1)^2 + (-1)^2)
Distance = sqrt(9 + 1 + 1)
Distance = sqrt(11)
Therefore, the length of the median through Q is sqrt(11).
The midpoint of PR can be found by taking the average of the x-coordinates, the y-coordinates, and the z-coordinates of P and R.
Midpoint of PR = ((2+8)/2, (3+5)/2, (9+3)/2) = (5, 4, 6)
Now, we can calculate the distance between the midpoint of PR and Q using the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Distance = sqrt((2-5)^2 + (5-4)^2 + (5-6)^2)
Distance = sqrt((-3)^2 + (1)^2 + (-1)^2)
Distance = sqrt(9 + 1 + 1)
Distance = sqrt(11)
Therefore, the length of the median through Q is sqrt(11).
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If P (2, 3, 9), Q (2, 5, 5) and R (8, 5, 3) are vertices of a triangle then find the length of median through Q.a)√24b)√38c)√11d)√53Correct answer is option 'C'. Can you explain this answer?
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