Question

Find a point on the x-axis which is equidistant from
the points (5,-2) and (-3,2).
the correct answer is 1,0​

Answer 1

Answer:

(1,0)

Step-by-step explanation:

As the point lies of x-axis, its y-coordinate is 0.

Let the point be (a, 0).

Using distance formula:

=> √(- 3 - a)² + (2 - 0)² = √(5 - a)² + (- 2 - 0)²

= > (-3 - a)² + 2² = (5 - a)² + 2²

= > (- 3 - a)² = (5 - a)²

= > (3 + a)² = (5 - a)²

= > 3 + a = 5 - a

= >>a + a = 5 - 3 = 2

= > 2a = 2

= > a = 1

Or, use mid point formula:

= > (a, 0) = (5-3/2 , -2+2/2)

= > (a, 0) = (2/2 , 0/2)

= > (a, 0) = (1, 0)

Hence the required point is (1,0)