Let r be the triangle with vertices at (x₁ ,y₁ ), (x₂ ,y₂), and (x₃ ,y₃). Show that
a) The area of triangle r can be calculated using the formula 1/2 times the absolute value of the determinant of the matrix formed by the coordinates of the vertices.
b) The perimeter of triangle r is the sum of the lengths of its three sides, which can be calculated using the distance formula.
c) The centroid of triangle r is the point (x₁+x₂+x₃/3, y₁+y₂+y₃/3).
d) The slope of one of the sides of triangle r is given by y₂ - y₁ / x₂ - x₁.