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Co-Ordinate Geometry — Maths STD 10 — Question

Gujarat BoardEnglish MediumSTD 10MathsCo-Ordinate Geometry4 Marks
Question
If the point $A(0, 2)$ is equidistant from the points $B(3, p)$ and $C(p, 5)$, find $P.$
✓

Answer

The given points are $A(0, 2), B(3, p)$ and $C(p, 5).$
$ A B=A C \Rightarrow A B^2=A C^2 $
$ \Rightarrow(3-0)^2+(p-2)^2=(p-0)^2+(5-2)^2 $
$ \Rightarrow 9+p^2-4 p+4=p^2+9 $
$ \Rightarrow 4 p=4 \Rightarrow p=1$
$\text { Hence, } p=1$

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