Mathematics, 09.01.2020 19:31 ElizabethF

15 points and will mark brainliest

what is the area of the composite figure whose vertices have the following coordinates?

(−8,3) , (−4,4) , (−1,1) , (−4,−2) , (−8,−2)

enter your answer in the box.

2.the coordinates of the vertices of a polygon are (−2, −1) , (2, 3) , (4, 3) , (4, −3) , and (−1, −4) .

round each side length to the nearest tenth of a unit.

enter the perimeter of the polygon in the box.

Answers: 3

Show answers

Answers

1) The area of the composite figure whose vertices have the coordinates (−8,3) , (−4,4) , (−1,1) , (−4,−2) , (−8,−2) is (20 + 4 + 3) = 27 unit²

Step-by-step explanation:

1) Given : coordinate of a composite figure (−8,3) , (−4,4) , (−1,1) , (−4,−2) , (−8,−2)

We have to find the area of the composite figure whose vertices have the given coordinates.

We first plot the given coordinate and obtained the figure as shown in attachment below.

Join points (−8,3) and (−4,−2)

and (−4,4) and (−4,−2)

Thus, we have obtained three triangles.

Area of triangle having coordinates (a_x,a_y),(b_x,b_y),(c_x,c_y) is given by ,

$\left | \frac{a_x(b_y-c_y)+b_x(c_y-a_y)+c_x(a_y-b_y}{2} \right |$

Thus, for triangle with coordinate (−8,3) ,(-8, -2)and (−4,−2)

Area is given by

$\left | \frac{-8(-2+2)+(-8)(-2-3)+(-4)(3-(-2)}{2} \right |$

thus area for triangle with coordinate (−8,3) ,(-8, -2)and (−4,−2) is 20 unit²

Similarly, for triangle with coordinate (−8,3) ,(-4,-4)and (−4,−2)

Area is given by

$\left | \frac{-8(-4+2)+(-4)(-2-3)+(-4)(3-(-4)}{2} \right |$

thus area for triangle with coordinate (−8,3) ,(-8, -2)and (−4,−2) is 4 unit²

Similarly, for triangle with coordinate (−1,1) ,(-4,-4)and (−4,−2)

Area is given by

$\left | \frac{-1(-4+2)+(-4)(-2-1)+(-4)(1-(-4)}{2} \right |$

thus area for triangle with coordinate (−8,3) ,(-8, -2)and (−4,−2) is 3 unit²

Thus, the area of the composite figure whose vertices have the coordinates (−8,3) , (−4,4) , (−1,1) , (−4,−2) , (−8,−2) is (20 + 4 + 3) = 27 unit²

Given : The coordinates of the vertices of a polygon are (−2, −1) , (2, 3) , (4, 3) , (4, −3) , and (−1, −4) .

We have to find the perimeter of the polygon.

We first plot these point to obtain the polygon.

Using distance formula $\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$

thus, we find the distance between each two points using above formula,

we have

a) $\mathrm{Distance\:between\:}\left(-2,\:-1\right)\mathrm{\:and\:}\left(2,\:3\right)$

$=\sqrt{\left(2-\left(-2\right)\right)^2+\left(3-\left(-1\right)\right)^2}=4\sqrt{2}=5.7$

$\mathrm{The\:distance\:between\:}\left(2,\:3\right)\mathrm{\:and\:}\left(4,\:3\right)\mathrm{\:is\:}$

$=\sqrt{\left(4-2\right)^2+\left(3-3\right)^2}=2$

$\mathrm{The\:distance\:between\:}\left(4,\:3\right)\mathrm{\:and\:}\left(4,\:-3\right)\mathrm{\:is\:}$

$=\sqrt{\left(4-4\right)^2+\left(-3-3\right)^2}=6$

$\mathrm{The\:distance\:between\:}\left(4,\:-3\right)\mathrm{\:and\:}\left(-1,\:-4\right)\mathrm{\:is\:}$

$=\sqrt{\left(-1-4\right)^2+\left(-4-\left(-3\right)\right)^2}=\sqrt{26}=5.1$

$\mathrm{The\:distance\:between\:}\left(-1,\:-4\right)\mathrm{\:and\:}\left(-2,\:-1\right)\mathrm{\:is\:}$

$=\sqrt{\left(-2-\left(-1\right)\right)^2+\left(-1-\left(-4\right)\right)^2}=\sqrt{10}=3.2$

thus, perimeter is sum of all distance is 22 units.

Thus, the perimeter of the coordinates of the vertices of a polygon are (−2, −1) , (2, 3) , (4, 3) , (4, −3) , and (−1, −4) is 22 units.

15 points and will mark brainliest what is the area of the composite figure whose vertices have the

Answer from: Quest

Try a or d, hope that

Answer from: Quest

What do you mean by that?

Another question on Mathematics

Mathematics, 21.06.2019 13:30

The equation y=mx+b is the slope-intercept form of the equation of a line. what is the equation solved for b? y-m=b y-mx=b y/mx=b y/m-x=b

Answers: 2

Answer

Mathematics, 21.06.2019 14:10

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. the mean arrival rate is 10 passengers per minutes. compute the following probabilities. p(x = 4) p(x > 11)

Answers: 2

Answer

Mathematics, 21.06.2019 19:00

John used linear combination to solve the system of equations shown. he did so by multiplying the first equation by -3 and the second equation by another number to eliminate the x-terms. what number did jonas multiply the second equation by? 4x-6y=23x+5y=11

Answers: 2

Answer

Mathematics, 21.06.2019 19:40

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Answers: 3

Answer

You know the right answer?

15 points and will mark brainliest

what is the area of the composite figure whose verti...

Questions