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3 years ago

Find the area of the following shape. you must show all work to receive credit.

Mathematics

1 answer:

Margaret [11]3 years ago

3 0

Answer:

Step-by-step explanation:

Use the Pick's theorem

Let P be a polygon in the plane whose vertices have integer coordinates. Then the area of P can be determined just by counting the lattice points on the interior and boundary of the polygon!

In fact, the area is given by

$A=i+\dfrac{b}{2}-1$

where i is the number interior lattice points, and b is the number of boundary lattice points.

Look at the picture.

$i=50,\ b=16$

Substitute:

$A=50+\dfrac{16}{2}-1=50+8-1=57$

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Given the coordinates below, what is the midpoint of AB? A(-6, -10) B(2,5)

madreJ [45]

Given :

$\:$

A(-6, -10)
B( 2, 5)

$\:$

$\gray{ \frak{The \: given \: two \: \: points \: are(x_{1 },y_{1})=(−6 , -10)and(x_{ 2 },y_{2} )=( 2,5 )\:}}$

$\:$

Let's solve by using midpoint formula :

$\:$

$\bf \boxed{\color{red}\frak{Midpoint \: \: Formula : {( \: x ,\:y \: ) = }( \frak{ \frac{x_{1 } + y_{1}}{2} , \frac{x_{2 } + y_{2}}{2} )}}}$

$\:$

$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -6 + 2}{2} , \frac{ - 10 + 5}{2} )}}$

$\:$

$\: \large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \frac{ -4}{2} , \frac{ - 5}{2} )}}$

$\:$

$\large \gray{ \frak{( \: x ,\:y \: ) = }( \frak{ \cancel\frac{ -4}{2} , \cancel\frac{ - 5}{2} )}}$

$\: \:$

$\underline{ \boxed{ \large \red{ \frak{option \: d }( \frak{ - 2, - 2.5)}}}}✓$

Hope Helps! :)

6 0

2 years ago

⚠️⚠️ help would be appreciated ⚠️⚠️

Pachacha [2.7K]

Answer:

(I rotated the trapezoid on the origin)

T' (-2, 2)

R' (-2, 5)

A' (-6, 2)

P' (-7, 5)

Step-by-step explanation:

The original points of the trapezoid were (2, -2), (2, -5), (6, -2) and (7, -5). Flipping trapezoid TRAP on the origin has the x and y coordinates showing their opposites from the original. So, find the opposite of each x and y coordinate to get the coordinates of the rotated trapezoid T'R'A'P'.

5 0

3 years ago

Two payment options to rent a car: You can pay $20 a day plus 25¢ a mile (Option A) or pay $10 a day plus 50¢ a mile (Option B).

BaLLatris [955]

You must drive more than 40 miles to make option A the cheaper plan

Solution:

Two payment options to rent a car

Let "x" be the number of miles driven in one day

You can pay $20 a day plus 25¢ a mile (Option A)

25 cents is equal to 0.25 dollars

OPTION A : 20 + 0.25x

You pay $10 a day plus 50¢ a mile (Option B)