Find the area of a right-angled triangle ABC (angle C = 90 degrees) if A (5; 7) B (5; -3) C (1; -1)

Points A and B have a coordinate x = 5, so side AB is parallel to the ordinate axis. If from point C we lower the height h to the side AB, then this height will be perpendicular to AB and parallel to the abscissa axis. The length of the hypotenuse AB and the height dropped from point C to it can be easily determined as the difference of the corresponding coordinates in absolute value.

a) AB = 7 – (-3) = 10.

Because any point on the segment AB will have abscissa 5, and point C has coordinates (1; -1), then:

h = 5 – 1 = 4.

S = 1/2 * h * AB, S = 1/2 * 4 * 10 = 20 cm2.

Answer: a triangle has an area of 20 cm2.