If the point A(0, 2) is equidistant from the points

Question:

If the point A(0, 2) is equidistant from the points B(3, p) and C(p, 5), find p.    

 

Solution:

The given points are A(0, 2), B(3, p) and C(p, 5).

$A B=A C \Rightarrow A B^{2}=A C^{2}$

$\Rightarrow(3-0)^{2}+(p-2)^{2}=(p-0)^{2}+(5-2)^{2}$

$\Rightarrow 9+p^{2}-4 p+4=p^{2}+9$

$\Rightarrow 4 p=4 \Rightarrow p=1$

Hence, p = 1.

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