Question

If the point$(x,y)$ is equidistant from points (3, 5) and (7, 1) , then $y$ = _____.

• A. $x+2$
• B. $x-1$
• C. $x-2$
• D. $x+1$

Answer 1

The correct option is C $x-2$

Let point $P(x,y)$ be equidistant from points $A(3,5)$ and $B(7,1).$

Distance, $d=\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

$\therefore AP=BPA{P}^2=B{P}^2(x-3{)}^2+(y-5{)}^2=(x-7{)}^2+(y-1{)}^2{x}^2-6x+9+y^2-10y+25=x^2-14x+49+y^2-2y+18x-8y=16x-y=2\therefore y=x-2$