Three of the vertices of quadrilateral MARY are M (-3,1), A(3,3), and R(5,7). Find the
coordinates of Y, such that, quadrilateral MARY is a parallelogram.
Use coordinate geometry to prove that MARY is a parallelogram.
Answers
9514 1404 393
Answer:
Y = (-1, 5)
Step-by-step explanation:
The diagonals of a parallelogram bisect each other, so have the same midpoint. That is ...
(M +R)/2 = (A +Y)/2
Y = M + R - A . . . . . . multiply by 2 and subtract A
Y = (-3, 1) +(5, 7) -(3, 3) = (-3 +5 -3, 1 +7, -3) . . . . . substitute point coordinates
Y = (-1, 5)
Coordinate geometry was used to find Y that makes MARY a parallelogram. The fact that there is a solution is proof enough that MARY is a parallelogram.
_____
Your teacher may expect the "proof" to be either or both of ...
showing opposite sides have the same slopeshowing opposite line segments have the same lengthGiven the method used above, both of these are unnecessary. However, in the interest of completeness, we will demonstrate.
Slope and Length of MA
slope = (3 -1)/(3 -(-3)) = 2/6 = 1/3
length = √(2²+6²) = √40
Slope and Length of AR
slope = (7 -3)/(5 -3) = 4/2 = 2
length = √(4² +2²) = √20
Slope and Length of RY
slope = (5 -7)/(-1 -5) = -2/-6 = 1/3 . . . . same as opposite side MA
length = √((-2)²+(-6)²) = √40 . . . . . . . same as opposite side MA
Slope and Length of YM
slope = (1 -5)/(-3 -(-1)) = -4/-2 = 2 . . . . same as opposite side AR
length = √((-4)² +(-2)²) = √20 . . . . . . same as opposite side AR
Opposite sides have the same slopes, so the figure is a parallelogram.
Opposite sides have the same lengths, so the figure is a parallelogram.
Related Questions
what is the slope of (-3,5) and (2,0)
Answers
Answer:
is there anymore to the question?
Step-by-step explanation:
The population of a small town is changing at a rate of —255 people per year. How long will it take for the change in population to be —2,040 people?
Answers
Answer:
Solution in photo
Step-by-step explanation:
20 points
Determine whether the statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement.
To solve the system below by substitution, replace y in the second equation with 7−6x.
6x−y=7
2x+y=5
This statement is true.
This statement is false. To solve the system by substitution, replace x in the second equation with 7−6x.
This statement is false. To solve the system by substitution, replace y in the first equation with 7−6x.
This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.
Answers
Answer:
To solve the system below by substitution, replace y in the second equation with 7−6x.
==> False
This statement is false. To solve the system by substitution, replace x in the second equation with 7−6x.
==> False.
This statement is false. To solve the system by substitution, replace y in the first equation with 7−6x.
==> False
This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.
==> True.
From the first equation, 6x-y=7
y= 6x-7
Answer: This statement is false. To solve the system by substitution, replace y in the second equation with 6x−7.
Rewrite the following polynomial in standard form.
1 + 10x3 + x2
Answers
Answer:
31 + x
Step-by-step explanation:
1) 1 + 10 × 3 + x
2) 1 + 30 + x
3) 31 + x
Answer:
X2+10x3+1....…...…............
What is 6/-1 expressed as an integer?
Answers
Answer:
-6
Step-by-step explanation:
O salário de um artista é calculado através da função y = 2000 + 500x onde Y representa o valor total em Reais recebido em um mês de trabalho e "x" o número de shows realizados no mês. Qual foi o salário desse artista no mês em que realizou 12 shows?
Answers
Answer:
The artist's salary in the month is 8000.
Step-by-step explanation:
The salary of an artist is given by the function :
y = 2000 + 500x ....(1)
where Y represents the total amount in Reais received in a month of work and "x" the number of shows performed in the month.
We need to find the artist's salary in the month she performed 12 shows.
Put x = 12 in equation (1)
y = 2000 + 500(12)
= 2000 + 6000
= 8000
Hence, the artist's salary in the month is 8000.
Courtney needs to find 2,495 ÷ 48. In which place should she write the first digit of the quotient?
A. Ones
B. tens
C. Hundreds
D. Thousands
Answers
Answer:
Tens
Step-by-step explanation:
The 5 in 51 should be above the nine
Answer:
B.
Step-by-step explanation:
2,495 ÷ 48 is 51.97
the tens is the largest place value so thats where you would start
This is the one i need help with help and explain
Answers
Answer:
Step-by-step explanation:
count all the full squares... 12
and add 1/2 a square for the angled one
12.5 :) or 12 1/2
Answer: 12.5 sq units
Step-by-step explanation:
Make two triangles (big and small triangle) and one rectangle. ( kinda like what's in the pic)
Area of big triangle:
b = 3 h = 3
1/2 x 3 x 3 = 4.5 sq units
Area of small triangle:
b = 2 h = 2
1/2 x 2 x 2 = 2 sq units
Area of rectangle:
l = 3 w = 2
3 x 2 = 6 sq units
Area of the figure: A. of rect. + A. of s. tri. + A. b. tri.
6 + 2 + 4.5 = 12.5 sq units
Which equation has the slope of -2/7 and contains the point (5,-6)?
Answers
Answer:
i would go for B
Step-by-step explanation:
Describe the relationship between the two quantities. WILL GIVE BRAINLIEST NO JOKE ANSWERS PLEASE..
Answers
Answer:
Between the two quantities, the sales have a longer increase rate for dollars than the bicycle has for speed, and the bicycle travel had a good speed rate, but slowed down the increased again.
Step-by-step explanation:
Mark tried to pour 36 ounces of tea into 3 cups. after filling the cup to the top, there were still 13.5 ounces left in his tea pot. if each cup is the same size how much is in the tea cup? HELP PLEASE!
Answers
Answer:
its 12
Step-by-step explanation:
12 oz
Answer:
22.5/3
Step-by-step explanation:
Hey, the idea is to set up an equation that you can solve
36 ounces of tea = 3 cups(some ounces of tea) + 13.5 ounces left
Now just solve for how much tea is in each cup.
36-13.5 = 3(X)
3X = 22.5
x = 22.5/3
8 to the 7th power/ 8 to the second power
Answers
Answer: 32768 or [tex]8^5[/tex].
Step-by-step explanation:
[tex]8^7[/tex]= 8x8x8x8x8x8x8 = 2097152
[tex]8^2[/tex]= 8x8 = 64
Dividing Exponents
When you divide exponents with the same base. You subtract. So in this case, you subtract 7 by 2, (being exponents). The same base is 8. So your subtracting [tex]8^7[/tex] by [tex]8^2[/tex]. Which will get you [tex]8^5[/tex].
Dividing Whole Numbers.
You are going to divide whole numbers. Its pretty self explanatory but I will do the math for you anyways.
64 goes into 2097152, 32768 times. Or we can say,
2097152 divided by 64 = 32768.
So the answer is 32768, or [tex]8^5[/tex].
Linda needs to have her car towed. Little Town Auto charges a flat fee of $75 plus $2 per miletowed. Write a function expressing Linda's towing cost, C, in terms of miles towed, x. Find thecost of having a car towed 14 miles.
Answers
The cost of having a car towed 14 miles is $103.
To express Linda's towing cost, C, in terms of miles towed, x, we can use the given information that Little Town Auto charges a flat fee of $75 plus $2 per mile towed.
The function for the towing cost, C, can be written as:
C(x) = 75 + 2x
Where x represents the number of miles towed.
To find the cost of having a car towed 14 miles, we substitute x = 14 into the function:
C(14) = 75 + 2(14)
C(14) = 75 + 28
C(14) = 103
Therefore, the cost of having a car towed 14 miles is $103.
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How do you write 872.8% as a decimal?
Answers
Answer:
.82
Step-by-step explanation:
Answer:
8.728
Step-by-step explanation:
"Percent" means "per 100" or "over 100". To convert 872.8% to a decimal rewrite 872.8 percent in terms of per 100 or over 100.
A ladder rests 22 feet up the side of a building. If the base of the ladder is 20 feet away from the building, how tall is the ladder to the nearest hundredth?
Answers
Answer:
Length of ladder =L =15
Distance from wall = D =9
Height on wall = H =??
Pythagoras equation L*L = D*D + H*H
15×15= (9×9) + H×H
225-81 = 144 =HxH
H= 12 feet.
I am right or wrong
please check
Please help 0.8t+0.6t-t
Answers
Answer:
0.4t
Step-by-step explanation:
1.4t-t=0.4t
Hope this helps :)
Answer:
0.4t
Step-by-step explanation:
0.8t + 0.6t = 1.4t
1.4t-1t=0.4t
The diagram shows the governing system of a municipal government.
What does the diagram show about the strong mayor system?
The city council is elected and the mayor is not.
The mayor is elected and the city council is not.
The mayor has more power than the city council.
The city council shares equal power with the mayor.
Answers
Answer:
where is the diagram
Step-by-step explanation:
?
Answer:
C !!! THE MAYOR HAS MORE POWER THAN THE CITY COUNCIL !!!
Step-by-step explanation:
Please I need help
What is the perimeter of the parallelogram
Answers
Jody works at an ice cream counter. The ice cream costs $3 per cone. Let c represent the number of ice cream cones she sells. Let p represent
the total cost paid by the customers.
Choose two correct statements about the variables in this situation,
A. The cost per cone depends on the number of cones sold.
B. The total cost paid by customers depends on the number of cones sold,
O c The number of cones sold is independent of the total cost paid by customers.
D. The total cost paid by customers is independent of the number of cones sold,
Answers
Answer:
B and C are correct Hope this helps <3
Step-by-step explanation:
Answer:
B and C?
Step-by-step explanation:
Im a little unsure about C but im about99% sure that is correct
what are the next 3 terms of the sequence-3, -7, -11, -15?
Answers
Answer:
-19,-23,-27
Step-by-step explanation:
When looking at the original sequence you can see that it decreases by 4 every number, so just keep subtracting 4 to get the next numbers.
Answer: -19, -23, -27
Step-by-step explanation:
<33
Write an inequality that is represented by the graph.
Answers
Answer:
ff
Step-by-step explanation:
You spend 264 dollars on clothes. Shirts cost 24 and pants cost :2 you buy a total of 9 items
Answers
EQUATIONS:
24x + 32y = 264
x + y = 9
x is shirts, y is pants
SOLVING by substitution:
x = 9 - y
24(9 - y) + 32y = 264
216 - 24y + 32y = 264
8y = 48
y = 6
x + 6 = 9
x = 3
Need help ASAP!! I'll give brainliest to the correct answer!!!
A.) 18.7 units
B.) 10.5 units
C.) 9 units
D.) 13 units
Answers
Answer:
B.) 10.5
Step-by-step explanation:
Use ratios, but be careful.
AE/AD = AB/AC
14/18 = x/(x+3).
14x+42 = 18x
42 = 4x
x = 10.5
The value of x in the given figure is 10.5 so, option B.) 10.5 units is correct.
What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b
or
[tex]\dfrac{a}{b}[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
Using ratios;
AE/AD = AB/AC
14/18 = x/(x+3).
14x+42 = 18x
42 = 4x
x = 10.5
Thus, option B.) 10.5 units is correct.
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tom goes on hoilday south africa
Answers
Answer:
Yes, good for him. lol
Step-by-step explanation:
Answer:
what he do there?
use the quadratic formula to solve for x. 3x^2+9x+4=0
Answers
Answer:
x=−3/2 +1/6√33 or x=−3/2 + −1/6√33Step-by-step explanation:
Let's solve your equation step-by-step.
3x2+9x+4=0
For this equation: a=3, b=9, c=4
3x2+9x+4=0
Step 1: Use quadratic formula with a=3, b=9, c=4.
x=−b±√b2−4ac/2a
x=−(9)±√(9)2−4(3)(4)/2(3)
x=−9±√33/6
what does b equal. 2/3b +19=35
Answers
2/3b + 19 = 35
-19 -19
----------------------
2/3b = 16
÷2/3 ÷2/3
----------------------
b = 24
answers for both boxes please
Answers
Answer:
(x,y)=(4,-1)Step-by-step explanation:
[tex]hope \: it \: helps[/tex]
Without looking, Luke picks necklace beads from a bag of 52 beads. Half the beads are rough. The other half are smooth. There are 13 red beads, 13 blue beads, 13 green beads, and 13 black beads.
What is the theoretical probability of selecting a rough bead?
Answers
The theoretical probability of selecting a rough bead is 1/2.
Total number of beads = 52
Number of rough beads = 26
Number of smooth beads =26
What is the probability?Probability is the measurement of possibilities.
P(event) = favorable outcomes/total outcomes
P(rough) = number of rough beads/ total beads
P(rough) =26/52
P(rough) =1/2
Therefore, the theoretical probability of selecting a rough bead is 1/2.
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Answer: 1/2
Step-by-step explanation:
what is 1256x - 14x + 16x simplified
Answers
Answer:1
1258
Step-by-step explanation:
Do like terms.
Answer:
The answer was 1258
Step-by-step explanation:
1256x - 14x + 16x
add similar elements = 1256x - 14x + 16x
1258
Which two properties characterize an air mass?
Answers
Answer:
Step-by-step explanation: Air masses are given a two-part name that describes the humidity and temperature characteristics of the region where they form
Answer:
Air masses have fairly uniform temperature and moisture content in horizontal direction (but not uniform in vertical).
Step-by-step explanation:
Looked it up
