Which point lies on a circle with a radius of 5 units and center at p(6, 1)?
a.
q(1, 11)
b.
r(2, 4)
c.
s(4, -4)
d.
t(9, -2)

B

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (6, 1) and r = 5, thus

(x - 6)² + (y - 1)² = 25 ← equation of circle

To determine which point lies on the circle, substitute the coordinates into the left side and if equal to the right side then point is on the circle

A (1, 11)

(1 - 6)² + (11- 1)² = (- 5)² + 10² = 25 + 100 = 125 ≠ 25 ← not on circle

B (2, 4)

(2 - 6)² + (4 - 1)² = (- 4)² + 3² = 16 + 9 = 25 ← lies on circle

C (4, - 4)

(4 - 6)² + (- 4 - 1)² = (- 2)² + (- 5)² = 4 + 25 = 29 ≠ 25 ← not on circle

D (9, - 2)

(9 - 6)² + (- 2 - 1)² = (- 3)² + (- 3)² = 9 + 9 = 18 ≠ 25 ← not on circle

The only point that lies on the circle is R(2, 4)

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.