Final answer:
To find the point in the graph of y=(x)¹/² that is closest to the point (5,0), use the distance formula √((x₂-x₁)²+(y₂-y₁)²). Simplify the equation to a quadratic equation and find the value of x that minimizes the distance.
Step-by-step explanation:
To find the point in the graph of y=(x)¹/² that is closest to the point (5,0), we need to find the point on the graph that has the smallest distance from (5,0). The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula: d = √((x₂-x₁)²+(y₂-y₁)²).
For the given equation, y=(x)¹/², the x-coordinate of any point on the graph will be x, and the y-coordinate will be √x. Therefore, the distance equation becomes: d = √((x-5)²+(√x-0)²). Simplifying this equation will give us a quadratic equation, which can be solved by finding the value of x that minimizes the distance.
Since the question does not provide the domain for the graph, we can assume x≥0. By minimizing the distance between the given point (5,0) and the graph of y=(x)¹/², we can find the point on the graph that is closest to (5,0).