1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dovator [93]
3 years ago
7

The coordinates of polygon ABCD are A(-4,-1), B(-2,3), C(2,2), and D(4,-3). Use these coordinates to complete the sentences belo

w. The perimeter of polygon ABCD, to the nearest thousandth, is units. If point D were translated 2 units up and 1 unit to the left to create point D', the perimeter of polygon ABCD', to the nearest thousandth, would be units.
Mathematics
1 answer:
PolarNik [594]3 years ago
8 0

Answer:

The perimeter of polygon ABCD, to the nearest thousandth units is

22.227 units

The perimeter of polygon ABCD', to the nearest thousandth, would be 20.980 units

The area of polygon ABCD' is 19.5 units²

Step-by-step explanation:

The coordinates forming the polygon are

A (-4,-1), B(-2,3), C(2,2), and D(4,-3)

The perimeter then is given by the sum of the length of the sides as follows;

Length of line between two X and Y points distance, xi and yj apart is

length XY =  \sqrt{x^2+y^2}

Therefore, the length between points AB is

length AB = \sqrt{(-4 - (-2))^2+(-1-3)^2}

= \sqrt{(-4 +2)^2+(-4)^2} = \sqrt{-2^2+-4^2}  = \sqrt{20}  = 4.472 units

Similarly, length BC is given by

Length BC =  \sqrt{(-4)^2+1^2} =  \sqrt{17} = 4.123 units

Length CD = \sqrt{(-2)^2+5^2} =  \sqrt{29} = 5.385 units

Length DA = \sqrt{(8)^2+(-2)^2} =  \sqrt{68} = 8.246 units

The perimeter is equal to;

length AB + Length BC + Length CD + Length DA

= 4.472 + 4.123 + 5.385 + 8.246 = 22.227 units

If the point D is moved up 2 units and left 1 unit we have

D' = x-1, y+2 where x and y are the coordinates of point D

D(4, -3) → D'((4-1), (-3+2)) = D'(3, -1)

The length D'A =  \sqrt{(7)^2+(0)^2} =  \sqrt{49} =7 units

The perimeter of polygon ABCD'

length AB + Length BC + Length CD + Length D'A

= 4.472 + 4.123 + 5.385 + 7 = 20.980 units.

The area is given by the determinant of the 3 by 3 matrix using Cramer's Rule as follows

 S_{\bigtriangleup} = (\frac{1}{2})|x_1y_2+x_2y_3+x_3y_1-x_1y_3-x_2y_1-x_3y_2|

= (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

Triangle ABC we have

A(-4,-1)

B(-2,3)

C(2,2)

S_{{\bigtriangleup}ABC} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

=(\frac{1}{2})|(-4)(3-2)+(-2)(2-(-1)) +2((-1)-3)|

= =(\frac{1}{2})|-4-6 -8|= 9 units^2

Triangle ACD'

A(-4,-1)

C(2,2)

D'(3, -1)

S_{{\bigtriangleup}ACD'} = (\frac{1}{2})|x_1(y_2-y_3)+x_2(y_3-y_1) +x_3(y_1-y_2)|

=(\frac{1}{2})|(-4)(2+1)+(2)(-1+1) +3((-1)-2)| = \frac{21}{2} = 10.5 units²

Area of polygon =   S_{{\bigtriangleup}ABCD'} = S_{{\bigtriangleup}ABC} + S_{{\bigtriangleup}ACD'} = (9 + 10.5) units²

Area of polygon ABCD' = 19.5 units².

You might be interested in
If the points (0, 0), (-1, 1), and (-2, 2) lie on the graph of function h, then which of the following rules could represent the
attashe74 [19]
The function is modulus cause the range of function consists of non-negative numbers with the same magnitude.so the second one is the answer
3 0
3 years ago
Read 2 more answers
On a piece of paper, sketch △ABC with m∠A=30° , m∠B=60° , and m∠C=90° . Which statements about the triangle are true? Select eac
gladu [14]

Answer:

Step-by-step explanation:i dont know duuu

6 0
3 years ago
A line passes through (−1, 7) and (2, 10).
Murljashka [212]
The formula is y=mx+b
To get the slope or m, use this formula
(the second y minus the first y)/(the second x minus the first x)
Now set it up.
(10-7)/(2--1)
3/3=slope is 1.
y=1x+b

Insert one of the points for x and y.
i will do (-1,7)
7=1(-1)+b
7=-1+b
8=b
Insert this into the final equation:
y=1x+8

Try it out. If you're not sure, try both points. If it works, then you set it up correctly.
6 0
3 years ago
Read 2 more answers
Ok this has nothing to so with my assignments or anything but i have a serious question please help so my question is....
umka2103 [35]
If she is stated in the will she can. If not, then she can't unless You simply give it to her once you inherit the money.
5 0
3 years ago
Someone pls help me with this im new thats why tysm if you do help!!:)
Kipish [7]

Answer:

-8 hope this helps

Step-by-step explanation:

7 0
3 years ago
Other questions:
  • Can you help me find the slope for #2
    12·2 answers
  • Find the difference ( 9/4​x+6) − (− 5/4​x−24)=​
    6·1 answer
  • A bakery uses 475 pounds of apples to make 1000 apple tart each tart contains the same amount of apples how many pounds of apple
    9·2 answers
  • I need help again thanks it's the picture ​
    8·1 answer
  • What is the value of the expression below when z=2<br><br> 4z2-3z-4 please help
    11·1 answer
  • •Find the degree of each monomial<br>5x²<br> ​
    11·1 answer
  • Help me on this math question please
    13·2 answers
  • Pls help urgently extra points and mark brainlist
    8·1 answer
  • Freshman, sophomore, junior, and senior students at a high school will be surveyed regarding a potential increase in the extracu
    10·1 answer
  • Please help! I’ll mark you brainlist
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!