Answer:
(a) 47.5 square units
Step-by-step explanation:
You want the area of the triangle with vertices A(-7, 3), B(5, 8) and C(0, -2).
Sides
The sides of the triangle can be represented by the vectors ...
AB = B -A = (5, 8) -(-7, 3) = (12, 5)
and
AC = C -A = (0, -2) -(-7, 3) = (7, -5)
Area
The area is half the absolute value of the cross product of these vectors:
Area = 1/2|(12, 5) × (7, -5)|
= 1/2|(12(-5) -(5)(7)) = 1/2|-60 -35|
= 95/2 = 47.5
The area of the triangle is 47.5 square units.
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Additional comment
The 2-dimensional vector cross product of (a, b) and (c, d) is the scalar (ad -bc).
There are numerous methods of finding the area of a triangle when coordinates are given. We find this method to be one of the easiest, as we avoid computing any side lengths or angles.
