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
Anton [14]
3 years ago
11

I really need help with this.

Mathematics
1 answer:
aniked [119]3 years ago
3 0

9514 1404 393

Answer:

  a.  (1.4, 2.6)

  b.  (3, 2)

Step-by-step explanation:

a. The circumcenter is the intersection point of the perpendicular bisectors of the sides of the triangle.

For points X(a, b) and Y(c, d), the perpendicular bisector of XY can be written as ...

  (c -a)(x -(c+a)/2) +(d -b)(y -(d+b)/2) = 0

Then the equation of the perpendicular bisector of MN is ...

  (-2-4)(x -(-2+4)/2) +(4-0)(y -(4+0)/2) = 0

  -6(x -1) +4(y -2) = 0

  3x -2y = -1 . . . .  divide by -2 and put in standard form

Similarly, the perpendicular bisector of NO is ...

  (0-(-2))(x -(0-2)/2) +(6 -4)(y -(6+4)/2) = 0

  2(x +1) +2(y -5) = 0

   x + y = 4 . . . . divide by 2 and put in standard form

So, the point of intersection is ...

  (3x -2y) +2(x +y) = (-1) +2(4) . . . . . add twice the 2nd equation to the 1st

  5x = 7 . . . . . . simplify

  x = 1.4 . . . . . . divide by 5

  y = 4-1.4 = 2.6 . . . . . find y from the second equation

The coordinates of the circumcenter are (1.4, 2.6).

__

b. The centroid is the average of the vertex coordinates.

  centroid = (A +B +C)/3 = ((1, 2) +(3, 4) +(5, 0))/3 = (1+3+5, 2+4+0)/3 = (9, 6)/3

  centroid = (3, 2)

You might be interested in
If ABC is reflected across the y-axis, what are the coordinates of A?
Anon25 [30]

Answer:

A. (2,5)

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Solve -4(6×+3)=-12(x+10)​
OleMash [197]

Answer:

x = 9

Step-by-step explanation:

-4(6x+3)=-12(x+10)

-24x-12=-12x-120

       +12         +12

-12x=-12x-108

/-12    /-12    / -12

x=9

Answer x=9

5 0
2 years ago
What is the slope of this line?<br><br> A 1/3<br> B -3<br> C 3<br> D -1/3
aleksandr82 [10.1K]
The slope is 3 so the answer would be 3. Hope it helps! :)
4 0
2 years ago
Read 2 more answers
Given f (x) = 2x² +1evaluate f (-1).
soldi70 [24.7K]

Answer:

3

Step-by-step explanation:

f(x) = 2x^2 + 1

f(-1) means that wherever you see an x on the right hand side, you substitute -1.

f(-1) = 2(-1)^2 + 1 = 2 + 1 = 3

8 0
2 years ago
Read 2 more answers
What is the range of the data in this stem-and-leaf plot?
sergij07 [2.7K]
The range is the difference between the lowest and the highest number.

the answer is 30.5
3 0
3 years ago
Read 2 more answers
Other questions:
  • A sign on the pumps at a gas station encourages customers to have their oil checked, and claims that one out of 8 cars needs to
    15·1 answer
  • ASAP! LOVE YOU! THANKS! Will give Brainliest!
    6·1 answer
  • Figure PQR is an equilateral triangle with a semicircle attached to it. What is the perimeter of figure PQR? Use 3.14 to approxi
    9·1 answer
  • What is the equation for 1.2×5 in fractions
    5·2 answers
  • If your income is ​$27 a​ month, the price of pizza is​ $5 and the price of a video is​ $4, how many pizzas will you buy and how
    11·2 answers
  • Find the height, H, of the triangle shown
    13·1 answer
  • Which number is bigger 5.66 or 5.661?
    13·2 answers
  • Which of the following numbers is between0.40 and 0.47?
    5·2 answers
  • Patel squeezed oranges so that his family could have fresh-squeezed juice for breakfast. He squeezed 4/17 cups from the first or
    14·1 answer
  • If Leah is 6 years older than Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue?​
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!