The midpoints of the four sides of a rectangle are (-3,0), (2,0), (5,4), and (0,4). What is the area of the rectangle? (A) 20 (B) 25 (C) 40 (D) 50 E) 80

B) 25 is the correct answer.

Step-by-step explanation:

Finding the distance between the points,

(-3,0) and (2,0)

d² = (2+3)² + (0-0)²

or, d²= 5² + 0²

or, d² = 25

so, d = 5

Now,

(2,0) and (5,4)

d² = (5-2)² + (4-0)²

d² = 3²+4²

or, d² = 9 + 16

or, d² = 25

so, d = 5

Again,

(5,4) and (0,4)

d² = (0-5)² + (4-4)²

or, d² = -5² + 0²

or, d² = 25

so, d = 5

(-3,0) and (0,4)

d² = (0+3)²+(4-0)²

or, d² = 3²+4²

or, d² = 9+16

or, d² = 25

so, d = 5

Area = l×b

= 5×5

= 25

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

-10i^2-4i

step-by-step explanation:

evaluate for p=2,q=5i

(2−4)(2+5i)i

(2−4)(2+5i)i

=−10i2−4i