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
Butoxors [25]
3 years ago
5

find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.

Mathematics
1 answer:
solniwko [45]3 years ago
8 0
Check the picture below, so, that'd be the square inscribed in the circle.

so... hmm the diagonals for the square are the diameter of the circle, and keep in mind that the radius of a circle is half the diameter, so let's find the diameter.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
\stackrel{diameter}{d}=\sqrt{[-8-(-2)]^2+[-3-5]^2}
\\\\\\
d=\sqrt{(-8+2)^2+(-3-5)^2}\implies d=\sqrt{(-6)^2+(-8)^2}
\\\\\\
d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10

that means the radius r = 5.

now, what's the center?  well, the Midpoint of the diagonals, is really the center of the circle, let's check,

\bf \textit{middle point of 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{-8-2}{2}~,~\cfrac{-3+5}{2} \right)\implies (-5~,~1)

so, now we know the center coordinates and the radius, let's plug them in,

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}\\
&-5&1&5
\end{array}
\\\\\\\
[x-(-5)]^2-[y-1]^2=5^2\implies (x+5)^2-(y-1)^2=25

You might be interested in
Which shows the rational expression written using the least common denominator?x-2/x^3
Gelneren [198K]

Answer:

Multiply 2/3 and your number. If you have a whole number, convert it to a fraction by putting it over a denominator of 1. When multiplying fractions, calculate numerator times numerator, then denominator times denominator. For example, to find two-thirds of 18, multiply 2/3 x 18/1 to get 36/3.

6 0
3 years ago
HELP DUE IN 10 MINUTES!!
Pavlova-9 [17]

Answer:

x intercept = 26

y intercept = 6.5

Step-by-step explanation:

n/a

3 0
2 years ago
Read 2 more answers
Solve the equation 1/2(16x – 6) = 2.
Lorico [155]

Answer:

x = 0.625 or 5/8

Step-by-step explanation:

1/2(16x-6) = 2

8x - 3 = 3

8x = 3 + 3

8x/8 = 9/8

x = 0.625

can you mark me as brainliest

6 0
2 years ago
Which is the simplified form of this expression?
Reika [66]

Answer:

C is the answer

Step-by-step explanation:

4 0
3 years ago
What is the average of the four smallest of integers ?
Elanso [62]
This question is easier than it seems. If there are 9 consecutive integers with the mean being 16, then 16 must be the median. So just add four on top and four below 16 to give you your range of 9 values, 12-20. 12+13+14+15+16+17+18+19+20=144, 144/9=16. So the mean of the first four numbers is (12+13+14+15)/4= 13.5. If you check, 13.5 is also the median of these four numbers.

 
6 0
3 years ago
Other questions:
  • 95% of 120 games played
    8·1 answer
  • If 4 × 8 = 32, then 32 divided by 8 must equal ___
    13·1 answer
  • What are the next 2 numbers in this geometric sequence<br><br> -512, -128, -32
    11·2 answers
  • somebody plz help me (the question i need help with is the one that is circled in pink and has the number 4)
    12·1 answer
  • Use the "rule of 72" to estimate the doubling time (in years) for the interest rate, and then calculate it exactly. (Round your
    5·1 answer
  • There are 1250 students in a school. 58% of them are female. How many are male?
    6·2 answers
  • Use the Associative Property of Addition to write an expression equivalent to (u + 2) + 8.
    12·1 answer
  • Help a brother out answering his question​
    14·1 answer
  • In a bag of candy, there are 6 blue pieces, 14 yellow pieces, and 5 green pieces. What is the ratio of green pieces to total pie
    6·2 answers
  • I need help with this please!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!