The line equally inclined to the coordinate axes and equidistant from points
$A (1, - 2) a n d B (3, 4) i s$

x + y = 2, x + y = 3

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x - y = 3, x - y = 1

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x - y = 1, x + y = 3

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x + y = 2, x - 3 = 3

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Solution

The correct option is B $x - y = 3, x - y = 1$
$\begin{matrix} slope = tan 45^{\circ} - (1) (+ 1, - 2) and (3, - 4) slope = \frac{- 2 + 4}{1 - 3} = - 1 midpoint = (\frac{1 + 3}{2}, \frac{- 2 - 4}{2}) = (2, - 3) \frac{y + 3}{x - 2} = 1 \Rightarrow y + 3 = x - 2 x - y = 5 \end{matrix}$

Hence, B is correct

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The line equally inclined to the coordinate axes and equidistant from points A(1,−2)andB(3,4)is

The correct option is B x−y=3,x−y=1 slope =tan45∘−(1)(+1,−2) and (3,−4) slope =−2+41−3=−1 midpoint =(1+32,−2−42)=(2,−3)y+3x−2=1⇒y+3=x−2x−y=5 Hence, B is correct

The line equally inclined to the coordinate axes and equidistant from points
$A (1, - 2) a n d B (3, 4) i s$