Question

Show that (4, 1) is equidistant from the points ( - 10, 6) and (9, - 13).

Answer 1

distance between point (4,1) & (-10,6) is
= √{(4 + 10)² + (1 - 6)²}
 = √(14² + 5²)
 = √221
distance between point (4,1) & (9,-13) is 
= √{(4-9)² + (1+13)²}
 = √(5²+14²)
= √221

Answer 2

We can find it by using the distance formula.
let us consider   A=(-10,6)   ; B=(9,-13)  ; C=(4,1)
we can say C is equidistant from A and B if AC=BC
AC=√(4+10)²+(1-6)² = √(14)²+(-5)² = √196+25 = √221
BC=√(4-9)²+(1+13)²=√25+196=√221
Since  AC = BC we can say C is equidistant from A and B