Final answer:
Triangle PQR is a scalene triangle.
Step-by-step explanation:
The given coordinates (P(-2,8), Q(2,4), and R(4,6)) represent the vertices of triangle PQR. We can find the distance between two points using the distance formula:
Distance = sqrt((x2-x1)^2 + (y2-y1)^2)
Using this formula, we can calculate the lengths of each side of the triangle and compare them to determine the type of triangle. In this case, we have:
PR = sqrt((-2-4)^2 + (8-6)^2) = sqrt(36+4) = sqrt(40)
PQ = sqrt((-2-2)^2 + (8-4)^2) = sqrt(16+16) = sqrt(32)
QR = sqrt((4-2)^2 + (6-4)^2) = sqrt(4+4) = sqrt(8)
Since none of the sides have the same length, triangle PQR is a scalene triangle.