Find the point on x-axis which is equidistant from the points A(3… - Vidyadip

Question

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

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Answer

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 $\sqrt{(3-\text{x})^2+(2-0)^2+(2-0)^2}=\sqrt{(5-\text{x})^2+(5-0)^2+(4-0)^2}$ $\Rightarrow9-6\text{x}+\text{x}^2+4+4=25-10\text{x}+\text{x}^2+25+16$ $\Rightarrow17-6\text{x}+\text{x}^2=66-10\text{x}+\text{x}^2$ $\Rightarrow4\text{x}=49$ $\Rightarrow\text{x}=\frac{49}{4}$ Hence, the required Point is $\Big(\frac{49}{4},\ 0,\ 0\Big)$

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