Final answer:
To identify points A and B for triangle ABC with a given slope and the condition that AB is horizontal, we apply the concept of slope for AC and the fact that the y-coordinate for point B must be the same as point C. The correct points for A and B are (-4,5) and (7,2) respectively.
Step-by-step explanation:
The student's question pertains to finding the possible coordinates for points A and B if triangle ABC is a right triangle with AC having a slope of 3, and segment AB being horizontal. Given that point C is at (6,2), we can calculate potential coordinates for A and B using the concept of slope and the fact that AB is horizontal (hence the slope is 0).
To find the possible points for A using the slope of AC, we use the formula of slope (m) which is obtained by the difference in y-coordinates divided by the difference in x-coordinates (m = (y2 - y1)/(x2 - x1)). With the slope of 3 and point C at (6,2), only the points that maintain this ratio are valid for point A. However, since AB is horizontal, any y-coordinate of B must match that of C, namely 2.
Using this information, we can determine that point A must be (-4,5) and point B must be (7,2), because these are the only points from the provided options that would result in a slope of 3 for segment AC and a horizontal line for segment AB.