Introduction to 3D coordinate geometry — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSIntroduction to 3D coordinate geometry3 Marks
Question
Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).
✓
Answer
Let $P(0, y, 0)$ be a point on $y$-axis which is equidistant from $Q(3,1,2)$ and $R(5,5,2)$.
So
$(P R)^2=(P Q)^2 \Rightarrow(0-5)^2+(y-5)^2+(0-2)^2=(0-3)+(y-1)^2+(0+2)^2$
$\Rightarrow 25+y^2+25-10 y+4=9+y^2+1-2 y+4$
$\Rightarrow-10 y+2 y=14-54$
$\Rightarrow-14 z-8 z=16-49$
$\Rightarrow-8 y=-40$
$\Rightarrow y=5$
so, the required point is $(0,5,0)$
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