Answer:
(x - 8)² + (y - 10)² = 36
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
<u>Pre-Calculus</u>
Circle Center Formula: (x - h)² + (y - k)² = r²
- <em>(h, k) </em>is center
- <em>r</em> is radius
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<em>(h, k)</em> = (8, 10)
<em>r</em> = 6
<u>Step 2: Find Equation</u>
- Substitute in variables [Center Circle Formula]: (x - 8)² + (y - 10)² = 6²
- Evaluate exponents: (x - 8)² + (y - 10)² = 36
Answer:
Step-by-step explanation:
Convert mixed numbers to improper fractions:
Add the fractions
Divide 64 by 5
What we know:
line P endpoints (4,1) and (2,-5) (made up a line name for the this line)
perpendicular lines' slope are opposite in sign and reciprocals of each other
slope=m=(y2-y1)/(x2-x1)
slope intercept for is y=mx+b
What we need to find:
line Q (made this name up for this line) , a perpendicular bisector of the line p with given endpoints of (4,1) and (2,-5)
find slope of line P using (4,1) and (2,-5)
m=(-5-1)/(2-4)=-6/-2=3
Line P has a slope of 3 that means Line Q has a slope of -1/3.
Now, since we are looking for a perpendicular bisector, I need to find the midpoint of line P to use to create line Q. I will use the midpoint formula using line P's endpoints (4,1) and (2,-5).
midpoint formula: [(x1+x2)/2, (y1+y2)/2)]
midpoint=[(4+2)/2, (1+-5)/2]
=[6/2, -4/2]
=(3, -2)
y=mx=b when m=-1/3 slope of line Q and using point (3,-2) the midpoint of line P where line Q will be a perpendicular bisector
(-2)=-1/3(3)+b substitution
-2=-1+b simplified
-2+1=-1+1+b additive inverse
-1=b
Finally, we will use m=-1/3 slope of line Q and y-intercept=b=-1 of line Q
y=-1/3x-1
