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 P.
- a)√24
- b)√38
- c)√11
- d)√53
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
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 QR is (5, 5, 4).
Length of median through P is distance between midpoint of QR and P i.e.
Midpoint of line QR is (5, 5, 4).
Length of median through P is distance between midpoint of QR and P 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 point P, we need to find the midpoint of the line segment QR, which will be the midpoint of Q and R.
The midpoint of two points can be found by averaging their coordinates. In this case, the midpoint of Q (2, 5, 5) and R (8, 5, 3) is ((2+8)/2, (5+5)/2, (5+3)/2) = (5, 5, 4).
Now, we can find the length of the line segment from P to the midpoint of QR.
The distance between two points in three-dimensional space can be found using the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
In this case, the coordinates of P are (2, 3, 9) and the coordinates of the midpoint are (5, 5, 4).
d = sqrt((5-2)^2 + (5-3)^2 + (4-9)^2)
= sqrt(3^2 + 2^2 + (-5)^2)
= sqrt(9 + 4 + 25)
= sqrt(38)
Therefore, the length of the median through P is sqrt(38).
The midpoint of two points can be found by averaging their coordinates. In this case, the midpoint of Q (2, 5, 5) and R (8, 5, 3) is ((2+8)/2, (5+5)/2, (5+3)/2) = (5, 5, 4).
Now, we can find the length of the line segment from P to the midpoint of QR.
The distance between two points in three-dimensional space can be found using the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2)
In this case, the coordinates of P are (2, 3, 9) and the coordinates of the midpoint are (5, 5, 4).
d = sqrt((5-2)^2 + (5-3)^2 + (4-9)^2)
= sqrt(3^2 + 2^2 + (-5)^2)
= sqrt(9 + 4 + 25)
= sqrt(38)
Therefore, the length of the median through P is sqrt(38).
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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 P.a)√24b)√38c)√11d)√53Correct answer is option 'B'. Can you explain this answer?
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