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TS EAMCET · Maths · Straight Lines

If the algebraic sum of the perpendicular distances from the points \((2,0),(0,2)\) and \((1,1)\) to a variable line is zero, then the variable line always passes through a fixed point. The coordinates of that point are

  1. A \((0,0)\)
  2. B \((2,0)\)
  3. C \((0,2)\)
  4. D \((1,1)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((1,1)\)

Step-by-step Solution

Detailed explanation

Let a variable line is ax + by \(+ c =0\) ...(i) now, perpendicular distance from \((2,0),(0,2)\) and \((1,1)\) to the line is respectively \( {d}_1=\frac{2 {a}+{c}}{2}, {~d}_2=\frac{2 {~b}+{c}}{2} \text { and }_3=\frac{{a}+{b}+{c}}{2} \) Since, \(d_1+d_2+d_3=0\)…