Answer:
Option C. 6 square units
Step-by-step explanation:
we know that
Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.
Let
a,b,c be the lengths of the sides of a triangle.
The area is given by:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
p is half the perimeter
p=[tex]\frac{a+b+c}{2}[/tex]
we have
Triangle ABC has vertices at A(-2,1), B(-2,-3), and C(1,-2)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
[tex]d=\sqrt{(-3-1)^{2}+(-2+2)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]dAB=4\ units[/tex]
step 2
Find the distance BC
[tex]d=\sqrt{(-2+3)^{2}+(1+2)^{2}}[/tex]
[tex]d=\sqrt{(1)^{2}+(3)^{2}}[/tex]
[tex]dBC=\sqrt{10}\ units[/tex]
step 3
Find the distance AC
[tex]d=\sqrt{(-2-1)^{2}+(1+2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(3)^{2}}[/tex]
[tex]dBC=\sqrt{18}\ units[/tex]
step 4
[tex]a=AB=4\ units[/tex]
[tex]b=BC=\sqrt{10}\ units[/tex]
[tex]c=AC=\sqrt{18}\ units[/tex]
Find the half perimeter p
p=[tex]\frac{4+\sqrt{10}+\sqrt{18}}{2}=5.70\ units[/tex]
Find the area
[tex]A=\sqrt{5.7(5.7-4)(5.7-3.16)(5.7-4.24)}[/tex]
[tex]A=\sqrt{5.7(1.7)(2.54)(1.46)}[/tex]
[tex]A=\sqrt{35.93}[/tex]
[tex]A=6\ units^{2}[/tex]
