Question

find a point on x-axis which is equidistant from A(-3,-4) B(4,-3)​

Answer 1

coordinates of a point on x axis = (x,o)

A---------------------------P---------------------------B

(-3,-4)                        (x,o)                            (4,-3)​

AP=BP

dist formula.

AP=√ (x2-x1)²+(y2-y1)²

AP=√(x- -3)²+(0- -4)²

AP=√(x+3)²+(4)²

AP=√x²+9+6x+16

AP=√x²+6x+25

BP=√(x-4)²+(0- -3)²

BP=√x²+16-8x+9

BP=√x²-8x+25

AP=BP

∴AP²=BP²

x²+6x+25=x²-8x=25

6x= -8x

6x+8x=0

14x=0

∴x=0

ie. P(0,0)