Answer:
50 square units
Step-by-step explanation:
You want the area of right triangle ABC, given A(-9, 10), B(7, -2) and C(4, -6).
Area
The area can be found from the coordinates as ...
Area = 1/2·|AB×CB|
The vector values are ...
AB = B-A = (7, -2) -(-9, 10) = (7+9, -2-10) = (16, -12)
CB = B-C = (7, -2) -(4, -6) = (7-4, -2+6) = (3, 4)
The cross product is found as ...
AB×CB = (16)(4) -(3)(-12) = 64 +36 = 100
So, the area is ...
Area = 1/2·|100| = 50 . . . . square units
The area of ∆ABC is 50 square units.
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Additional comment
A graph shows us the right angle is B, so we could also find the area as ...
A = 1/2bh
A = 1/2·|AB|·|CB| = 1/2·√(16²+(-12)²)·√(3²+4²)
A = 1/2·√400·√25 = (20·5)/2 = 50
We find the cross product formula takes less work. Also, it works with any pair of sides, not just the right-angle sides.
