Questions on Algebra: Matrices, determinant, Cramer rule answered by real tutors!

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Question 162512: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!
: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!

Answer by Fombitz(1789) About Me  (Show Source):
You can put this solution on YOUR website!
Let's graph the points.
drawing( 300, 300, -12, 2, -12, 2,grid( 1 ),circle( -8, -2, .2 ),<BR>
circle( -1, -11, .2 ),<BR>
circle( -1, -2, .2 ),<BR>
green(line(-1,-11,-1,-2)),<BR>
green(line(-1,-2,-8,-2)),<BR>
green(line( -8, -2, -1, -11)))
.
.
.
The area of a triangle is
A=(1/2)(bh)
where b is the base, h is the height of the triangle.
From the diagram,
b=7
h=9
A=(1/2)(bh)
A=(1/2)(7*9)
A=63/2=31.5
Your answer is correct.
Question 162512: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!
: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!

Answer by scott8148(2801) About Me  (Show Source):
You can put this solution on YOUR website!
yes, you are correct
Question 162512: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!
: Calculate the area of the triangle with the following vertices:
(-8, -2), (-1, -11), and (-1, -2)
I tried my best, and got an answer of 31.5 sq units. I just want to know if this is correct,and if not, see the steps to come to the correct answer and what it is. I thank you very much for your time!

Answer by josmiceli(2170) About Me  (Show Source):
You can put this solution on YOUR website!
First I want to see if any of the 3 lines that
connect these point is either horizontal or
vertical. that will just make the job easier
The pair of points (-1,-11) and (-1,-2) both have
the same x value, which makes the line between
them vertical.
The pair (-8,-2) and (-1,-2) have the same y value,
so the line between them is horizontal.
That means the triangle is a right triangle
The length of the 1st line is just the difference
between -11 and -2, which is 9
The length of the 2nd line is just the difference
between -8 and -1, which is 7
Using the formula A = (1/2)*b*h
A = (1/2)*9*7
A = 63/2
A = 31.5
Same as you got