Use determinants to find the area of the triangle with vertices at the given points. P(0, 0), Q(16, 0), R(16, 5)
A)A = 5
B)A = 80
C)A = 40
D)A = 16
E)none of these

Question

Quizplus · Accepted Answer

Let's call the three vertices P, Q, and R:

P = (0, 0)
Q = (16, 0)
R = (16, 5)

To find the area of the triangle, we can use the formula:

A = 1/2 * base * height

We can choose any side of the triangle as the base, but it's easiest to choose the one that is guaranteed to be horizontal (that is, the one between P and Q). The height of the triangle will be the perpendicular distance from point R to the line PQ.

The equation of line PQ is y = 0 (since it's the x-axis), so the perpendicular distance from R to PQ will just be the y-coordinate of point R.

Therefore, the base is 16 units long, and the height is 5 units.

Plugging these values into the formula, we get:

A = 1/2 * 16 * 5 
  = 40

So the area of the triangle is 40 square units. The best choice is therefore (C).

Use Determinants to Find the Area of the Triangle with Vertices