Question

K(-5,-2), M(5,4), S(-3,6), T(3,-4)

Answer 1

K(-5,-2) and M(5,4)
S(-3,6) and T(3,-4)
Let's calculate the slope m₁ of KM

m₁ = (y₂-y₁)/(x₂-x₁) → m₁ =(4+2)/(5+5) = 6/10 →m₁ = 3/5

Now let's calculate the slope m₂ of ST:
m₂ = (-4-6)/(3+3) → m₂ = (-10)/6 → m₂ = -5/3

We can conclude that KM and ST are perpendicular since thee product of their respective slopes (m₁).(m₂) = - 1
Proof: (3/5).(-5/3) = -15/15 = -1