Question

Which point on x-axis is equidistant from the points A(7, 6) and B(-3, 4) ?

(a) (0, 4) (b) (-4, 0) (c) (3, 0) (d) (0, 3)

Answer 1

Given points A(7,6) and B(-3,4)
Let the point be P(x,0) [we know that point on the x-axis is (x,0)]
So, AP = PB

and \(AP^2=PB^2\)
⇒

$49-9+36-16=6x+14x$
$40+20=20x$

$x=\frac{60}{20}$

⇒$x=3$
Hence, the point on the x-axis which is equidistant from the points A(7,6) and B(-3,4) is (3,0)
option c is correct