Question

The point on the X-axis which is equidistant from point A(4,6) and B(-1,3) is

• A. $(4.2,0)$
• B. $(4.5,0)$
• C. $(1.5,4.5)$
• D. $(1.5,0)$

Answer 1

The correct option is A

$(4.2,0)$

$\text{Let the coordinates of the point be (h,0) [since the point is on X-axis]}$

$\text{Applying distance formula}$

$(4-h{)}^2+(6-0{)}^2=(h+1{)}^2+(0-3{)}^2$

$(4-h{)}^2+36=(h+1{)}^2+9$

$16+h^2-8h+36=h^2+1+2h+9$

$52-8h=10+2h$

$10h=42$

$h=4.2$

$\therefore Thepointis(4.2,0).$