Question

Find the co-ordinates of the point on the x-axis which is equidistant from points (2,4) and (4,6), Also find the distance​

Answer 1

Step-by-step explanation:

Let the co-ordinates of the point on the x-axis be P(x, 0).

According to statement

P(x, 0) is equidistant from points A(2,4) and B(4,6)

Therefore, PA = PB

${PA}^{2} = {PB}^{2} \\ {(x - 2)}^{2} + {(0 - 4)}^{2} = {(x - 4)}^{2} + {(0 - 6)}^{2} \\ {x}^{2} + 4 - 4x + 16 = {x}^{2} + 16 - 8x + 36 \\ 4 - 4x = 36 - 8x \\ 4x = 32 \\ x = 8$

Hence, the co-ordinates of the point on the x-axis be P(8, 0).