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
goldfiish [28.3K]
3 years ago
14

Find the coordinates of the circumcenter of △PQR with vertices P(−2,5), Q(4,1), and R(−2,−3).

Mathematics
1 answer:
mel-nik [20]3 years ago
7 0

Answer: (1/3,2)

Step-by-step explanation:

Let O(x,y) be the circumference of the triangle PQR,

Thus, by the property of circumcenter all the vertices of the triangle are at same distance from this circumcenter.

Thus, PO = QO

By the distance formula,

(x+2)^2+(y-5)^2 = (x-4)^2+(y-1)^2

\impliesx^2+ 4x + 4 + y^2+ 25 - 10 y = x^2+16 - 8 x + y^2+1 - 2y

\implies 4x + 4 + 25 - 10 y = 16 - 8 x + 1 - 2y

\implies 4x +8x-10y+2y = 16 + 1 -25-4

\implies 12x - 8y = 17 - 29

\implies 12 x - 8 y = - 12---------(1)

Similarly, QO = RO

\implies (x-4)^2 + (y-1)^2 = (x+2)^2+(y+3)^2

\implies x^2 + 16 - 8x + y^2+ 1 - 2y = x^2+ 4 + 4 x +y^2+ 9 + 6 y

\implies 16 - 8x + 1 - 2y = 4 + 4 x + 9 + 6 y

\implies - 8x -4x-2y-6y=4+9-16-1

\implies -12 x - 8 y = 13 - 17

\implies 12 x + 8 y = 4   ------------(2)

By adding equation (1) and (2),

24 x = - 8

x = 1/3

By putting this value in equation (1),

We get,

Thus, 4 - 8 y = -12

8 y = 16

y = 2

You might be interested in
Turner mesuares 3/4 foot of a ribbon for a coustume. He needs 9 pieces of ribbon with the same length
AlekseyPX
That answer is 6.75
7 0
3 years ago
Read 2 more answers
3x(x − 2) + 2 x=6<br> i really need help
neonofarm [45]
This equation if finding x would be 88
8 0
2 years ago
What is the value of u and v?
Novay_Z [31]

Answer and Explanation:

Since this is an isosceles right triangle, you can use the ratio of side lengths specific to this type of triangle where both legs are the hypotenuse over root 2:

u = v = 164√2 / √2 = 164

so:

u = 164

v = 164

3 0
2 years ago
Read 2 more answers
The sum of partial products is equal to the final product?
Shkiper50 [21]
The sum of partial product is not always equal to a final product

8 0
3 years ago
Find k such that the equation kx^2+x+25k=0 has a repeated solution.
Paha777 [63]
Ill try to answer your question
4 0
3 years ago
Other questions:
  • What is (9 x 10 ^-3)^2 in scientific notation
    15·1 answer
  • The 5th and the 18th term of an a.p are 40 and 102 respectively calculate
    8·1 answer
  • Which values are solutions to the inequality below? <br><br>Check all that apply.<br><br>x2 &gt; 36
    9·2 answers
  • Kellen​'s boat travels 15 mph. find the rate of the river current if she can travel 2 mi upstream in the same amount of time she
    6·2 answers
  • Solve for AB. Round your answer to the nearest tenth if necessary.
    10·2 answers
  • Help me please!!!!!​
    10·1 answer
  • A circle has a circumference of approximately 113.04 inches. What is the diameter and the radius of the circle.
    6·1 answer
  • Which is bigger, one fourth of 16 or one third of 24?
    12·2 answers
  • Question 1: 3/4➗1/32
    10·1 answer
  • Angle 2 is 2x+10 angle 4 is 4x+80 solve for x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!