Final answer:
To locate point C in the triangle ABC with the given conditions, there are two possible y-coordinates for C, either 11 or 1. The exact x-coordinate cannot be determined without further information but should be between -2 and 8.
Step-by-step explanation:
In the graph of triangle ABC with vertices A=(-2,6) and B=(8,6), and given that the altitude from point C is 5, we want to determine the location of point C. Since the altitude (perpendicular) from C to AB must be a vertical line (because A and B have the same y-coordinate), point C will also have the same y-coordinate as A and B, which is 6. The altitude of 5 will be the distance on the y-axis from the line AB to point C.
Since the y-coordinate of AB is 6, and the altitude adds 5, point C's y-coordinate must be either 6 + 5 = 11 or 6 - 5 = 1. To find the x-coordinate, we note that the line AB is horizontal, so the x-coordinate for C can be any value as it will not affect the altitude. However, since a triangle's altitude must intersect with the base AB, the x-coordinate of C is also the x-coordinate where the altitude meets the base AB. If we assume that the triangle is not a degenerate triangle, then C cannot be directly above A or B on the graph, and instead will have an x-coordinate between -2 and 8.
There will be two possible locations for point C: either directly above or below the line AB, at the same x-coordinate where the altitude meets AB. Therefore, we would have two solutions: C1=(x,11) or C2=(x,1) where x is between -2 and 8. Without additional information to specify where the altitude meets AB, we cannot determine the exact x-coordinate for point C.