Question

What is the value of a if the point (3,5)(7,1)are equidistance from the point (a,0)?

Answer 1

Given,
$\sqrt{ {(a - 3)}^{2} + {(0 - 5)}^{2} } = \sqrt{ {(a - 7)}^{2} + {(0 - 1)}^{2} } \\ {(a - 3)}^{2} + {(- 5)}^{2} = {(a - 7)}^{2} + { (- 1)}^{2} \\( {a}^{2} - 6a + 9) + 25 = ({a}^{2} - 14a + 49) + 1 \\ 8a = 16 \\ a = 2$