SOLUTION: Given A(-3,2), B(-1,4) and C(1,-2), find the area of triangle ABC. Please have clear steps and working out thanks!

Click here to see ALL problems on Length-and-distance

Question 1011268: Given A(-3,2), B(-1,4) and C(1,-2), find the area of triangle ABC.
Please have clear steps and working out thanks!
Found 2 solutions by solver91311, Boreal:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Step 1: Use the slope formula to calculate the slope of the lines that contain each of the three line segments that form the sides of the triangle.

Step 2: Two of the slopes calculated in step 1 (given correct arithmetic) will be negative reciprocals of each other. The two lines that have these slopes will be perpendicular, and therefore the two line segments contained in these lines will be the legs of a right triangle. Determine which of the two sides of the triangle are the legs, that is, which are perpendicular to each other.

Step 3: Use the Distance Formula to calculate the length of each of the perpendicular segments identified in step 2.

Leave your answers in exact (radical) form.

Step 4: Multiply the two values calculated in step 3 together and then divide the product by 2. The result will be the desired area.

John

My calculator said it, I believe it, that settles it

Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Draw the triangle. It's worth finding all the slopes, in case one is perpendicular to another. Then there is a right triangle, and the area is much easier to find.
The slope of AB is -2/-2 =1
The slope of AC is 4/-4=-1
Therefore AB is perpendicular to AC, and we have a right triangle.
AB is the altitude if you draw it, and the distance using the distance formula is sqrt(2^2+2^2)or sqrt (8)
AC is the base, and its distance is sqrt(4^2+4^2=sqrt(32)
Area is 1/2bh=1/2 sqrt(8)(sqrt(32)=1/2*sqrt(256); sqrt (256)=16
Area is 1/2 *16=8 units.