Coordinate geometry question that appeared in section B of CBSE maths board paper in 2018. Solving the question requires knowledge of the section formula. Two parts to solving the question and both parts use the section formula.
Question 10: Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, - 3). Hence find m.
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Let P (4, m) divide A (2, 3) and B (6, 3) in the ratio k : 1.
The x-coordinate of a point P that divides a line segment joining points A(x1, y1) and B(x2, y2) in the ratio k : 1 is \\frac{kx_{2} + x_{1}}{k + 1})
Part 1: Compute the ratio in which point P divides the line segment AB
Apply the section formula to the x-coordinate of point P
In this question, x1= 2 and x2 = 6
∴ \\frac{6k + 2}{k + 1}) = 4
6k + 2 = 4(k + 1) 6k + 2 = 4k + 4 2k = 2 or k = 1 If k = 1, p divides the segment AB in the ratio 1 : 1
So, p is the midpoint of AB.
Part 2: Compute the y-coordinate of point P to find the value of 'm'
Y coordinate of P = \\frac{y_{1} + y_{2}}{2}) = \\frac{3 - 3}{2}) = 0
m = 0
Suppose the point P(4, m) divides the line segment joining the points A(2, 3) and B(6, -3) in the ratio K : 1
Co-ordinates of the point,
P = 6K + 2K + 1, -3K + 3K + 1
But the co-ordinates of point P are given as (4, m)
6K + 2K+1 = 4 ....(i)-3K + 3K+1 = m ..... (ii)6K + 2 = 4K +42K =2K =1Putting K =1 in equ. (2)-3(1) + 31 + 1 = m∴ m = 0Ratio is 1:1 and m = 0i.e P is the mid point of AB
Find the ratio in which P 4, m divides the line segment joining the points A 2,3 and B 6, 3. Hence find m.
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