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CBSE Class 10 Basic Math 2025 All Sets Solved Paper

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Question : 6 of 20
Marks: +1, -0
The point (x, 0) divides the line segment joining the points (-4, 5) and (0, -10) in the ratio
Solution:  
According to the Section formula, if a point P(x, y) that lies on a line Segment AB joining points A(x1,y1)A(x_{1}, y_{1}) and B(x2,y2)B(x_{2}, y_{2}) divides the line in the ratio m :n, then the Coordinates can be.
Coordinates = (x, y) = (mx2+nx1m+n,my2+ny1m+n)\left( \frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n} \right).
Let the point P(x, 0) divide the segment joining A(- 4, 5) and B(0, - 10) in the ratio m :n, then
(x, 0) = (m×0+n(−4)m+n,m(−10)+n(5)m+n)\left( \frac{m \times 0 + n(-4)}{m+n}, \frac{m(-10)+n(5)}{m+n} \right)
0 = −10m+5nm+n\frac{-10m+5n}{m+n}
-10m + 5n = 0
-10m = -5n
mn=510\frac{m}{n} = \frac{5}{10}
mn=12\frac{m}{n} = \frac{1}{2}
m:n=1:2m:n = 1:2
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