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In which ratio does the point P (1, 2) divides the join of A (-2, 1) and B (7, 4)?
- a)1 : 2
- b)2 : 1
- c)2 : 3
- d)3 : 2
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In which ratio does the point P (1, 2) divides the join of A (-2, 1) a...
To find the ratio in which the point P (1, 2) divides the line segment AB, we can use the section formula.
The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m : n, then the coordinates of P can be found using the following formula:
Px = (mx2 + nx1)/(m + n)
Py = (my2 + ny1)/(m + n)
Given that A(-2, 1) and B(7, 4) are the endpoints of the line segment AB, and P(1, 2) is the point dividing AB in the ratio m : n, we can substitute the values into the section formula:
Px = (mx2 + nx1)/(m + n)
1 = (m*7 + n*-2)/(m + n)
Py = (my2 + ny1)/(m + n)
2 = (m*4 + n*1)/(m + n)
Simplifying these equations, we get:
7m - 2n = m + n
4m + n = 2m + 2n
Rearranging the first equation, we have:
6m = 3n
2m = n
Substituting 2m for n in the second equation:
4m + 2m = 2m + 2(2m)
6m = 6m
This shows that the equations are consistent and valid for any value of m. Therefore, the ratio in which the point P divides the line segment AB is m : n = 1 : 2.
Hence, the correct answer is option A) 1 : 2.
The section formula states that if a line segment AB is divided by a point P(x, y) in the ratio m : n, then the coordinates of P can be found using the following formula:
Px = (mx2 + nx1)/(m + n)
Py = (my2 + ny1)/(m + n)
Given that A(-2, 1) and B(7, 4) are the endpoints of the line segment AB, and P(1, 2) is the point dividing AB in the ratio m : n, we can substitute the values into the section formula:
Px = (mx2 + nx1)/(m + n)
1 = (m*7 + n*-2)/(m + n)
Py = (my2 + ny1)/(m + n)
2 = (m*4 + n*1)/(m + n)
Simplifying these equations, we get:
7m - 2n = m + n
4m + n = 2m + 2n
Rearranging the first equation, we have:
6m = 3n
2m = n
Substituting 2m for n in the second equation:
4m + 2m = 2m + 2(2m)
6m = 6m
This shows that the equations are consistent and valid for any value of m. Therefore, the ratio in which the point P divides the line segment AB is m : n = 1 : 2.
Hence, the correct answer is option A) 1 : 2.
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Community Answer
In which ratio does the point P (1, 2) divides the join of A (-2, 1) a...
Let the ratio be k:1.
⇒ 6k = 3
⇒ k = 3/6 = 1/2
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