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

A = 20 units ^ 2

Explanation:

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

Answer 2

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