Final answer:
To find three points that are equidistant from F(4,0) and the line y=x, we need to find points that are equidistant from F and lie on a line perpendicular to y=x.
Step-by-step explanation:
To find three specific points that are equidistant from the point F(4,0) and the line y=x, we need to find three points that are equidistant from F and lie on a line perpendicular to the line y=x.
Since the line y=x has a slope of 1, the perpendicular line will have a slope of -1.
We can choose any value for x and find the corresponding y-coordinate for three equidistant points. For example, if we choose x=5, the corresponding y-coordinate will be -1. So one point is (5,-1).