The Cartesian plane and the distance formula

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Learn it Points are (x, y). Quadrants: I (+, +), II (−, +), III (−, −), IV (+, −). Distance: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Use squared lengths to test for equal sides or right angles.

Example: Is the triangle A(0, 0), B(4, 0), C(0, 3) right-angled?

AB² = 16, AC² = 9, BC² = 16 + 9 = 25.
$16 + 9 = 25$.
Yes: a right angle at A (Pythagoras).

Loading questions…