This might be a little difficult to show without a picture, but I'll do my best.

First graph the points on the coordinate plane and connect the dots to make a triangle.

**To find the perimeter of the triangle you need to use the distance formula.**

Distance = √( ( y_{2}-y_{1 })^{2} + ( x_{2}-x_{1 })^{2})

I'll show how to do this for length RS.

RS = √( ( 5-(-3))^{2} + ( 0 - (-4))^{2})

RS = √( 8^{2} + 4^{2})

RS = √80 = 8.94

The rest of the sides I'll leave to you.

**Next is the area.**

The area of a triangle = 1/2 *b *h

If we use the base (RT) then the height will be the distance between the point S and the line RT.

When drawn this is fairly obvious that the distance will be 8, but it will not always be obvious.

One formula to find the area of a triangle from three points is:

Area = [A_{x}(B_{y} - C_{y}) + B_{x}(C_{y} - A_{y}) + C_{x}(A_{y} - B_{y})] /2

Solving this you will get 44 square units.

Lastly is the centroid which involves following the steps above.

The midpoint of TR (or RT these are the same line) can be found by averaging the x and y coordinates.

(Also known as adding them together then dividing by two.

Point N will be ([7 + (-4)] /2 , [-3 + (-3)] /2)

Point N is (1.5,-3)

Next we connect Point N to S.

The centroid appears on this line where 2/3 of the line is above it and 1/3 of the line is below it.

First we find the difference between the x coordinates and y coordinates.

Diff X = 0-(1.5) = -1.5

Diff Y = 5- (-3) = 8

Then multiply each by 1/3.

-1.5 * 1/3 = -0.5

8 * 1/3 = 8/3 = 2.667

Finally add these to the value N to get point C

C = (1.5 + (-0.5), -3 + 8/3)

C = (1,-1/3) **This is the centroid.**

*If you prefer to start with point S instead you would multiply Diff X and Y by 2/3 and subtract their values from S.*

Hopefully this explains the problem well enough. If you have any questions feel free to ask.

Jon S.

07/06/20