Q.Without using Pythagoras theorem show that points A(4,4), B(3, 5) and C(−1, −1) are the vertices of a right angled triangle.

The slope of a line is the tangent of its inclination — the angle θ the line makes with the positive X-axis, measured anticlockwise, with 0° ≤ θ < 180°. So slope m = tanθ. Equivalently, for any two points on a non-vertical line, the slope equals the change in y divided by the change in x between them. A horizontal line has slope 0 (inclination 0°); a vertical line has undefined slope (inclination 90°, where tangent is undefined). Two lines are parallel exactly when they share the same slope, and two non-vertical lines are perpendicular exactly when the product of their slopes is −1 — a fact proved by relating the two lines' inclinations and using the tangent-difference identity. This single number, the slope, packa …