By using what we know about distances between points, we will see that y = 2.5
We know that the distance between the point (6, y) and (4, 1) is the same distance between (6, y) and the x-axis.
Remember that the distance between a point (x, y) and the x-axis is equal to y.
Then we will have that the distance between (6, y) and (4, 1) is equal to y.
So we need to solve:
[tex]distance = y = \sqrt{(6 - 4)^2 + (y - 1)^2} \\ \\y = \sqrt{4 + y^2 - 2y + 1} \\\\y^2 = 5 +y^2 - 2y \\\\0 = - 2y + 5[/tex]
So we need to solve:
2y = 5
y = 5/2 = 2.5
If you want to learn more about distances, you can read:
https://brainly.com/question/7243416
