Question

Find a point on the x-axis, which is
equidistant from the points (7 , 6) and (3,
4).

Answer 1

Answer:

(3,0)

Step-by-step explanation:

(3,0)

Let the point on the x-axis be (x,0)

Distance between (x,0) and (7,6)=

(7−x)

2

+(6−0)

2

=

7

2

+x

2

−14x+36

=

x

2

−14x+85

Distance between (x,0) and (−3,4)=

(−3−x)

2

+(4−0)

2

=

3

2

+x

2

+6x+16

=

x

2

+6x+25

As the point (x,0) is equidistant from the two points, both the distances

calculated are equal.

x

2

−14x+85

=

x

2

+6x+25

=>x

2

−14x+85=x

2

+6x+25

85−25=6x+14x

60=20x

x=3

Thus, the point is (3,0)