Question

Plot the points in the coordinate plane. Then find the perimeter and area of the polygon. A(-2, -1), B(1, -1), C(1, 4) A) Perimeter: 15 units, Area: 0 square units B) Perimeter: 12 units, Area: 7.5 square units C) Perimeter: 15 units, Area: 6 square units D) Perimeter: 14 units, Area: 7.5 square units"

Answer 1

To find the perimeter of the polygon, find the lengths of the sides and add them up. To find the area of the polygon, use the Shoelace formula. Perimeter: 14 units and Area: 7.5 square units. Therefore, the correct answer is D).

Step-by-step explanation:

To find the perimeter of the polygon, we need to find the lengths of the sides and then add them up.

Using the distance formula, we can calculate:

AB = sqrt((1-(-2))^2 + (-1-(-1))^2)

= sqrt(3^2 + 0^2)

= 3

BC = sqrt((1-1)^2 + (4-(-1))^2)

= sqrt(0^2 + 5^2)

= 5

AC = sqrt((1-(-2))^2 + (4-(-1))^2)

= sqrt(3^2 + 5^2)

= sqrt(9 + 25)

= sqrt(34)

Perimeter = AB + BC + AC

= 3 + 5 + sqrt(34)

To find the area of the polygon, we can use the Shoelace formula:

Area = 1/2 * |(-2*(-1) + 1*(-1) + 1*4 - (-1)*1 - (-2)*4 - 1*(-1))|

= 1/2 * |(-2 + 1 + 4 - (-1) - (-8) + 1)|

= 1/2 * |(-2 + 1 + 4 + 1 + 8 + 1)|

= 1/2 * |(15)|

= 1/2 * 15

= 7.5

Therefore, the correct answer is D).