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प्रश्न
Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.
उत्तर
Let (x1, y1) = (–1, 7) and (x2, y2) = (4, –3), m : n = 2 : 3.
According to the section formula,
`x = (mx_2 + nx_1)/(m + n)`
`x = (2 × 4 + 3 × (–1))/(2 + 3)`
`x = (8 – 3)/5`
`x = 5/5`
∴ `x = 1`
`y = (my_2 + ny_1)/(m + n)`
`y = (2 × (–3) + 3 × 7)/(2 + 3)`
`y = (–6 + 21)/(5)`
`y = (15)/(5)`
∴ y = 3
∴ The coordinate of points p is (1, 3).
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संबंधित प्रश्न
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Solution:
Here A(–1, 1), B(5, – 3), C(3, 5) and suppose D(x, y) are coordinates of point D.
Using midpoint formula,
x = `(5 + 3)/2`
∴ x = `square`
y = `(-3 + 5)/2`
∴ y = `square`
Using distance formula,
∴ AD = `sqrt((4 - square)^2 + (1 - 1)^2`
∴ AD = `sqrt((square)^2 + (0)^2`
∴ AD = `sqrt(square)`
∴ The length of median AD = `square`
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