I NEED A ANSWER SOON PLEASE!!! What is the area of a rectangle with vertices at (−4, 0), (−3, 1) , (0, −2), and (−1, −3)?

don't round any side lengths plz

6

Step-by-step explanation:

If you plot all 4 points, you will see that they are given in clockwise order around the rectangle.

If you take (-3, 1) and find the distance to (-4, 0), and take again (-3, 1) and find the distance to (0, -2), you will have the lengths of two consecutive sides. These sides can then be used as length and width to find the area.

distance from (-3, 1) to (-4, 0):

d = √[(-3 - (-4))² + (1 - 0)²] = √[1² + 1²] = √2

distance from (-3, 1) to (0, -2):

d = √[(-3 - 0)² + (1 - (-2))²] = √[(-3)² + 3²] = 3√2

area = LW = √2 × 3√2 = 3 × 2 = 6

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9