Q. Two points $A$ and $B$ have coordinates (1, 1) and $(3,\ - 2)$ rrespectively. The coordinates of a point at a distance $\sqrt{85}$ from $B$ on the line through $B$ perpendicular to $AB$, are

A) (4, 7)
B) (7, 4)
C) (5, 7)
D) $( - 5,\ - 3)$
Explanation

(c)
It is simple way to take a point from the option and finding the distance, which is equal to $\sqrt{85}$
Taking point $P(5,\ 7)$
$BP = \sqrt{(5 - 3)^{2} + (7 + 2)^{2}}$
$= \sqrt{4 + 81} = \sqrt{85}$
Hence, option (c) is correct
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Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.