Question

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

Answer 1

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