Question

find the value of k if the point p(o,2)is equidistant from (3,k)and(k,5)​

Answer 1

Step-by-step explanation:

The point p(o,2) is equidistant from (3,k) and (k,5)

∴√{(k-2)²+(3-0)²} = √{(5-2)²+(k-0)²}

=> (k-2)²+(3-0)² = (5-2)²+(k-0)²

=> k² + 4 - 4k + 9 = 9 + k²

=> 4k = 4

=> k = 1

* using the Distance Formula of Coordinate Geometry.

Answer 2

Answer:

$\sqrt{ {(3 - 0)}^{2} + {(k - 2)}^{2} } = \sqrt{ {(k - 0)}^{2} + {(5 - 2)}^{2} } \\ squaring \: both \: sides \\ 9 + {k}^{2} + 4 - 4k = {k}^{2} + 9 \\ 4k = 4 \\ k = 1$