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NDA 2019 Maths · Mathematics · Straight Lines · easy

A point P lies on the x-axis and is equally distant from the points A(1,2) and B(3,4). The abscissa of P is

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A point PP lies on the x-axis and is equally distant from the points A(1,2)A(1,2) and B(3,4)B(3,4). The abscissa of PP is
  1. A. 33
  2. B. 52\frac52
  3. C. 77
  4. D. 55
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Answer: (D) 55

Let P=(h,0)P=(h,0). Then PA2=PB2PA^2=PB^2 gives (h−1)2+4=(h−3)2+16(h-1)^2+4=(h-3)^2+16, i.e. −2h+5=−6h+25-2h+5=-6h+25, so 4h=204h=20 and h=5h=5. Check: PA2=16+4=20PA^2=16+4=20 and PB2=4+16=20PB^2=4+16=20. The value 52\frac52 is the midpoint's y-coordinate misread, and 33 is just BB's abscissa.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake