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A line segment with end points A(-6, 10) and B(3, -8) is divided in the ratio 2 : 7 by a point P. Find the coordinates of point P.
- a)(-6, 4)
- b)(-4, 6)
- c)(4, -4)
- d)(6, -6)
Correct answer is option 'B'. Can you explain this answer?
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A line segment with end points A(-6, 10) and B(3, -8) is divided in th...
If a line segment with end points A(x1, y1) and B(x2, y2) is divided in the ratio p : q by a point P(x, y).
For given condition
For given condition
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A line segment with end points A(-6, 10) and B(3, -8) is divided in th...
Understanding the Problem
To find the coordinates of point P that divides the line segment AB in the ratio 2:7, we use the section formula in coordinate geometry. Let's denote the coordinates of points A and B.
- A(-6, 10)
- B(3, -8)
Applying the Section Formula
The section formula states that if a point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of point P can be calculated as:
P(x, y) = [(mx2 + nx1) / (m+n), (my2 + ny1) / (m+n)]
Here, we have:
- m = 2 (part of A)
- n = 7 (part of B)
- x1 = -6, y1 = 10 (coordinates of A)
- x2 = 3, y2 = -8 (coordinates of B)
Calculating the Coordinates of Point P
1. Calculate x-coordinate:
P(x) = [(2 * 3) + (7 * -6)] / (2 + 7)
- = (6 - 42) / 9
- = -36 / 9
- = -4
2. Calculate y-coordinate:
P(y) = [(2 * -8) + (7 * 10)] / (2 + 7)
- = (-16 + 70) / 9
- = 54 / 9
- = 6
Final Coordinates of Point P
Thus, the coordinates of point P are:
P(-4, 6)
This matches option 'b' as stated in the question.
To find the coordinates of point P that divides the line segment AB in the ratio 2:7, we use the section formula in coordinate geometry. Let's denote the coordinates of points A and B.
- A(-6, 10)
- B(3, -8)
Applying the Section Formula
The section formula states that if a point P divides the line segment joining points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of point P can be calculated as:
P(x, y) = [(mx2 + nx1) / (m+n), (my2 + ny1) / (m+n)]
Here, we have:
- m = 2 (part of A)
- n = 7 (part of B)
- x1 = -6, y1 = 10 (coordinates of A)
- x2 = 3, y2 = -8 (coordinates of B)
Calculating the Coordinates of Point P
1. Calculate x-coordinate:
P(x) = [(2 * 3) + (7 * -6)] / (2 + 7)
- = (6 - 42) / 9
- = -36 / 9
- = -4
2. Calculate y-coordinate:
P(y) = [(2 * -8) + (7 * 10)] / (2 + 7)
- = (-16 + 70) / 9
- = 54 / 9
- = 6
Final Coordinates of Point P
Thus, the coordinates of point P are:
P(-4, 6)
This matches option 'b' as stated in the question.
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A line segment with end points A(-6, 10) and B(3, -8) is divided in the ratio 2 : 7 by a point P. Find the coordinates of point P.a)(-6, 4)b)(-4, 6)c)(4, -4)d)(6, -6)Correct answer is option 'B'. Can you explain this answer?
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