Question

find the perimeter of the polygon abcd that has its vertices at a(2, -2), b(6, -2), c(6, 6), and d(2, 6).
a) 12 units
b) 32 units
c) 64 units
d) 24 units

Explanation:

Step1: Identify the shape

Plot the points \( A(2, -2) \), \( B(6, -2) \), \( C(6, 6) \), \( D(2, 6) \). This is a rectangle since opposite sides are equal and all angles are right angles.

Step2: Calculate length of AB

For \( A(2, -2) \) and \( B(6, -2) \), the distance \( AB = |6 - 2| = 4 \) (since y-coordinates are the same).

Step3: Calculate length of BC

For \( B(6, -2) \) and \( C(6, 6) \), the distance \( BC = |6 - (-2)| = 8 \) (since x-coordinates are the same).

Step4: Calculate perimeter of rectangle

Perimeter of a rectangle is \( 2\times (length + width) \). Here, length \( = 8 \), width \( = 4 \). So perimeter \( = 2\times(4 + 8) = 2\times12 = 24 \).

Answer:

D) 24 units