Question

A triangle has vertices at (2, 3), (½ , –2), and (– 3, 2). What is the area of the triangle? please show me the steps. use determinants.

Answer 1

| x1 y1 1|
|x2 y2 1|* +/- 1/2
|x3 y3 1|
Is the formula to find the area of triangle using determinants.
Put the values:
|2 3 1|
|1/2 -2 1|
|-3 2 1|

Expand using 1st row,
2(-2-2)-3(1/2+3)+1(1-6)
-8-3(7/2)+1(-5)
-1/2(-8-21/2-5)
-1/2(-13-21/2)
-1/2(-47/2)
47/4 square units. is your answer.

NOTE: We are writing +1/2 or -1/2 because we need the final answer in +ve if it is -ve inside bracket, then we multiply by -1/2 to get positive answer and if not, +1/2. Hope this helps!

Answer 2

Thank you so much!