Question

E vertices of ∆ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ∆ABC is units, and its area is square units.

Answer 1

We can use the distance formula to calculate perimeter: $\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$ = Distance

From A to B: √232

From B to C: 10

From C to A: √52

10 + √232 + √52 = 10 + 2√58 + 2√13

Perimeter = 10 + 2√58 + 2√13 units

For Area we can use matrices, but since one of the sides is horizontal, we can just calculate with distance formula and area of triangle formula.

The area of a triangle formula is 1/2(h x b)

h=height

b=base

So the height is 6 and the base is 16. (I graphed it.)

16 * 6 = 96 96/2 = 48 Area: 48 square units.