Find the length of the side AB A (-8; 4) B (4; -5).

The coordinates of points A (-8; 4) and B (4; -5) are given.

To find the length of the segment AB, draw a right-angled triangle and find out how long its sides are. You can add point E (4; 4) or point D (-8; -5). The resulting triangles ABE and ABD will be equal, each of them will have AB as a hypotenuse. The lengths of the legs will be equal:

AE = BD = | – 8 | + | 4 | = 8 + 4 = 12,

AD = BE = | 4 | + | -5 | = 4 + 5 = 9.

Now the task sounds like this: find the length of the hypotenuse if it is known that the length of the legs is 9 and 12 units.

We solve by the Pythagorean theorem.

a² + b² = c²

9² + 12² = 81 + 144 = 225 = 15²

We found the length of the hypotenuse: AB = 15.

Answer: the length of the segment AB is 15 units.