Final answer:
The points (2,4) and (-4,-2) are not the endpoints of a diameter of a circle.
Step-by-step explanation:
The endpoints of a diameter of a circle are two points that lie on the circumference of the circle and are furthest apart from one another. To determine if the given points (2,4) and (-4,-2) are the endpoints of a diameter of a circle, we can measure the distance between them. Using the distance formula, we have:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the given points:
d = sqrt((-4 - 2)^2 + (-2 - 4)^2) = sqrt((-6)^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72) = 6*sqrt(2)
The distance between the given points is 6*sqrt(2). If this distance is equal to the length of the diameter of a circle, then the points are indeed the endpoints of a diameter of that circle.
Therefore, we can conclude that the points (2,4) and (-4,-2) are not the endpoints of a diameter of a circle.