Question

15

Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth.
The vertices of ABC are Al-2, 2), B6, 2), and 90, 8). The perimeter of ABC is
units, and its area is
square units.

Answer 1

9514 1404 393

Answer:

• perimeter: 22.81 units
• area: 24 square units

Explanation:

The lengths of the sides can be found using the distance formula.

d = √((x2 -x1)^2 +(y2 -y1)^2)

AC = √((0 -(-2))^2 +(8 -2)^2) = √(4+36) = 2√10

BC = √((0 -6)^2 +(8 -2)^2) = √(36+36) = 6√2

The distance AB is the difference of the x-coordinates of the points: 6-(-2) = 8.

Then the perimeter is ...

P = a + b + c = 6√2 +2√10 +8 = 8.49 +6.32 +8 = 22.81 . . . units

__

The height of the triangle is the difference in y-values between vertex C and line AB: 8 -2 = 6. The area is given by the formula ...

A = 1/2bh

A = 1/2(8)(6) = 24 . . . square units