Question

Find the point on x-axis which is equidistant from the points A (3, 2, 2) and B (5, 5, 4).

Answer 1

We know that the y and z coordinates of the point on the x-axis are 0.
So, let the required point be C (x, y, z)
Now, CA = CB

$$\begin{gathered} \sqrt{{\left(3-x\right)}^2+{\left(2-0\right)}^2+{\left(2-0\right)}^2}=\sqrt{{\left(5-x\right)}^2+{\left(5-0\right)}^2+{\left(4-0\right)}^2} \\ \Rightarrow 9-6x+x^2+4+4=25-10x+x^2+25+16 \\ \Rightarrow 17-6x+x^2=66-10x+x^2 \\ \Rightarrow 4x=49 \\ \Rightarrow x=\frac{49}{4} \end{gathered}$$
Hence, the required point is $\left(\frac{49}{4},0,0\right)$