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

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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

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

52 or what they said ☝️
4.) a skateboard ramp has a 142 degree entry angle. find the measure of

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