So the equation of a circle is (x - h)² + (y - k)² = r² where (h,k) are the coordinates of the center of the circle and r is the radius. The diameter of a circle is a line that goes from one point of the circle to the other through the center of the circle. Well the center would be midway through the diameter so use midpoint formula to find the center which is (h,k) Mid point formula is both given x's added together divided by 2 for h and both y coordinates added together divided by 2 to find k
(10+0)/2
10/2= 5
(12+2)/2
14/2 = 7
so the center of the circle is (5,7) now use distance formula using the center and one of the points to the radius
√((5-10)²+(7-12)²)
√(-5²+ -5²)
√(25 + 25)
√50 is the radius
Now plug all found information into circle equation
(x-5)² + (y-7)² =50 note the end is 50 because the circle equation is radius squared and since the radius is √50, radius² is 50.
Answer is c
Answer:
RQ = 9.
Step-by-step explanation:
m < RPQ = 180 - 90 - 75 = 15 degrees
m < PQM = 75 - 60 = 15 degrees.
So triangle PMQ is isosceles so side PM is congruent to side MQ, therefore MQ = 18.
Triangle RQM is a 30-60-90 triangle with RQ the shortest leg (because it is opposite the lowest angle) so that makes RQ = 1/2 of MQ. (The sides in a 30-60-90 triangle are in the ratio 1:sqrt3:2)
RQ = 1/2 * 18 = 9.
To reduce down a fraction you can try to find factors that go in both the numerator (top # of fraction) and denominator (bottom #)
So, for 6/9, 3 goes in both of them. When you divide each number by 3 you get:
2/3
You’re final answer would be 15/7 as an improper fraction or 2 and 1/7 as a mixed number.
The answer in an improper fraction is
47/36
As a mixed number, it is 1 11/36
Hope you become an expert at this soon :)
