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.
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