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
Gnoma [55]
3 years ago
6

32. Parallelogram ABCD has vertices A(0,0), B(2,4), and C(10,4). Find the coordinates of D.

Mathematics
1 answer:
goblinko [34]3 years ago
4 0

Answer:

The fourth vertex is D(8, 0)

Step-by-step explanation:

Let A(0, 0), B(2, 4), and C(10, 4) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a, b).

Join AC and BD. Let AC and BD intersect at point O.

  • We have known that the diagonals of a parallelogram bisect each other.  

So, O would be the midpoint of AC as well as that of BD.

A\left(0,\:0\right)=\left(x_1,\:x_2\:\right)

C\left(10,\:4\right)=\left(x_2,\:x_2\:\right)

The midpoint of AC is:

\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)

\left(x_1,\:y_1\right)=\left(0,\:0\right),\:\left(x_2,\:y_2\right)=\left(10,\:4\right)

=\left(\frac{10+0}{2},\:\frac{4+0}{2}\right)

=\left(5,\:2\right)

The midpoint of BD is:

=\left(\frac{a+2}{2},\:\frac{b+4}{2}\right)

so

∵  \frac{a+2}{2}=5

a+2=10

a=8

∵ \frac{b+4}{2}=2

b+4=4

b=0

Hence, the fourth vertex is D(8, 0)

You might be interested in
Calen is comparing the prices per child for hosting a birthday at Mr. Bob’s Buffet and Sally’s Pizza Safari.
madreJ [45]

The cost per child per child is $10 more at Mr Bob's buffet than it is at Sally's pizza safari.

Answer: Option 3.

<u>Explanation:</u>

According to the data and the information that has been given in the question, the cost of four children for this birthday party at Mr Bob is $60. But the cost of hosting a birthday party at Mr Sally is $50 which is the cost of four children.

So this tells us that the cost of hosting a birthday party is expensive at Mr Bob when compared to the cost of hosting a party at Mr Sally. It is $10 more than Mr Sally.

5 0
3 years ago
If one item cost $0.79 and I paid $3.16 at the register, how many items did I buy
Maurinko [17]

Answer:

You bought 4 items.

Step-by-step explanation:

3.16 divided by 0.79 = 4

8 0
3 years ago
Read 2 more answers
If triangle ABC defined by the coordinates A(1, 1), B(9, 1), C(1, 9) is dilated by a scale factor of 1 2 , with resulting vertex
AfilCa [17]

Answer: the answer is b (1, 1)

In this case, the center of dilation is a vertex of the original figure.  

The center of dilation is a fixed point in the plane about which all points are expanded or contracted.

Step-by-step explanation:

3 0
3 years ago
Which portion would you use to solve this problem?
atroni [7]

p\%=\dfrac{p}{100}\\\\4\%=\dfrac{4}{100}\\\\\dfrac{9}{x}=\dfrac{4}{100}\to\boxed{B.}

7 0
3 years ago
How can I isolate x in y=6x-2x²
ozzi

Answer:

x = 3/2 ± √(9/4 − 1/2 y)

Step-by-step explanation:

y = 6x − 2x²

First, factor out the leading coefficient:

y = -2 (x² − 3x)

Complete the square.

y = -2 (x² − 3x + 9/4 − 9/4)

y = -2 (x² − 3x + 9/4) + 9/2

y = -2 (x − 3/2)² + 9/2

Solve for x.

-1/2 y = (x − 3/2)² − 9/4

9/4 − 1/2 y = (x − 3/2)²

±√(9/4 − 1/2 y) = x − 3/2

x = 3/2 ± √(9/4 − 1/2 y)

8 0
3 years ago
Other questions:
  • their was only 1/2 pizza 3 needed 2 share it ... how much of the original pizza woud each person get please help right away!!!!!
    6·1 answer
  • Equation in slope intercept form of (-3,4) and (1,4)
    12·2 answers
  • Change 3 4/9 in to a decimal
    11·1 answer
  • Which of the following values for x and y make the equation 4x + 2y + 3 = 19 true?
    12·2 answers
  • Which property is BEST to use when simplifying (0.58 + 0.32) + 0.68?
    8·1 answer
  • A triangle inscribed in a semicircle can be identified as a/an _______ triangle.
    6·1 answer
  • Match the terms to their definition.
    8·2 answers
  • PLEASE ANY REAL PERSON WHO CAN HELP ME IVE BEEN WAITING LIKE 30 MINUTES
    13·1 answer
  • Work our the circumference of this circle
    10·1 answer
  • Please Help i Need this asap and i dont know
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!