 # Points A(-2,3), B(-5,-4), and C(2,-1) form triangle ABC on a coordinate plane. What is the area of this triangle in square units? 40 29 20

## Answers For this case we use the formula of distance between points:  d = root ((x2-x1) ^ 2 + (y2-y1) ^ 2)  We have then:  For AB:  AB = root ((- 5 - (- 2)) ^ 2 + (-4-3) ^ 2)  AB = 7.615773106  For AC:  AC = root ((2 - (- 2)) ^ 2 + (-1-3) ^ 2)  AC = 5.656854249  For BC:  BC = root ((2 - (- 5)) ^ 2 + (-1 - (- 4)) ^ 2)  BC = 7.615773106  The area is:  A = root ((s) * (s-a) * (s-b) * (s-c))  Where,  s = (a + b + c) / 2  Substituting values:  s = (7.615773106 + 5.656854249 + 7.615773106) / 2  s = 10.44420023  A = root ((10.44420023) * (10.44420023-7.615773106) * (10.44420023-5.656854249) * (10.44420023-7.615773106))  A = 20 units ^ 2  Answer:  The area of this triangle in square units is:  A = 20 units ^ 2

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