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प्रश्न
In the following example find the co-ordinate of point A which divides segment PQ in the ratio a : b.
P(–2, –5), Q(4, 3), a : b = 3 : 4
उत्तर
Let the coordinates of point A be (x, y).
P(–2, –5), Q(4, 3), a : b = 3 : 4
Using section formula
\[x = \frac{3 \times 4 + 4 \times \left( - 2 \right)}{3 + 4} = \frac{12 - 8}{7} = \frac{4}{7}\]
\[y = \frac{3 \times 3 + 4 \times \left( - 5 \right)}{3 + 4} = \frac{9 - 20}{7} = \frac{- 11}{7}\]
\[\left( x, y \right) = \left( \frac{4}{7}, \frac{- 11}{7} \right)\]
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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`
