Prove that the lines 2x + 3y + 8 = 0 and 27x – 18y + 10 = 0 are perpendicular to each other.

If the lines y = 3x + 7 and 2y + px = 3 are perpendicular to each other, find the value of p.

Without using Pythagoras Theorem, prove that the points A(1, 3), B(3, –1) and C(–5, –5) are the vertices of a right-angled triangle.

Without using distance formula, show that the points A(1, –2), B(3, 6), C(5, 10) and D(3, 2) are the vertices of a parallelogram.