Final answer:
The equidistant point on the x-axis from the points (1, 2) and (2, 3) is found using the distance formula; upon solving, it is determined to be (1.5, 0), corresponding to answer choice A.
Step-by-step explanation:
To find the point on the x-axis that is equidistant from the points (1, 2) and (2, 3), we can set up an equation based on the distance formula. The distance from any point (x, 0) on the x-axis to (1, 2) is equal to the distance from (x, 0) to (2, 3). We will denote this point as P(x, 0).
Using the distance formula, for the distance from P to (1, 2), we have:
√ ((x - 1) ^2 + (0 - 2) ^2) = √ ((x - 1) ^2 + 4)
For the distance from P to (2, 3), we have:
√ ((x - 2) ^2 + (0 - 3) ^2) = √ ((x - 2) ^2 + 9)
To find P, set the distances equal to each other:
√ ((x - 1) ^2 + 4) = √ ((x - 2) ^2 + 9)
Squaring both sides, we get:
(x - 1) ^2 + 4 = (x - 2) ^2 + 9
Expanding the squares, we have:
x^2 - 2x + 1 + 4 = x^2 - 4x + 4 + 9
Simplifying, x = 1.5
So, the equidistant point on the x-axis is (1.5, 0), which is answer choice A.