First slide

Equation of line in Straight lines

Question

$Suppose A, B are two points on 2 x - y + 3 = 0 and P (1, 2) is such that P A = P B, then the$ $mid-point of A B is$

Moderate

A

$(\frac{- 1}{5}, \frac{13}{5})$
B

$(\frac{- 7}{5}, \frac{9}{5})$
C

$(\frac{7}{5}, \frac{- 9}{5})$
D

$(\frac{- 7}{5}, \frac{- 9}{5})$

Solution

$Equation of A B i s 2 x - y + 3 = 0 W e h a v e Δ P A D ≅ △ P B D \Rightarrow D is foot of perpendicular from P to A B \begin{matrix} \Rightarrow \frac{α - 1}{2} = \frac{β - 2}{- 1} = \frac{- [2 \times 1 - 1 \times 2 + 3]}{4 + 1} \\ \Rightarrow \frac{α - 1}{2} = \frac{β - 2}{- 1} = \frac{- 3}{5} \\ α = \frac{- 1}{5}; β = \frac{13}{5} \\ D = (α, β) = (\frac{- 1}{5}, \frac{13}{5}) \end{matrix}$

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