Circle C lies on the coordinate plane with its center at (2,−16).
Point A(2,−13) lies on circle C.
Which equation verifies that the point P(−1,−16) lies on circle C?
a. (2−16)^2+(2−13)^2=(2−16)^2+(−1−16)^2
b. (2+1)^2+(−16+16)^2=(2−2)^2+(−16+13)^2
c. (2+16)^2+(−1+16)^2=(2+2)^2+(−16−13)^2
d. (2−1)^2+(−16−16)^2=(2+2)^2+(−16−13)^2
whats the answer.
it’s b
To determine which equation verifies that point P(-1, -16) lies on the circle C with center (2, -16), we need to use the distance formula to compare the distances between points A(2, -13), P(-1, -16), and the center of the circle C.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
We can start by calculating the distance between point A(2, -13) and the center of the circle (2, -16):
distance_A = sqrt((2 - 2)^2 + (-13 - (-16))^2)
distance_A = sqrt(0^2 + 3^2)
distance_A = sqrt(9)
distance_A = 3
Next, we can calculate the distance between point P(-1, -16) and the center of the circle (2, -16):
distance_P = sqrt((-1 - 2)^2 + (-16 - (-16))^2)
distance_P = sqrt((-3)^2 + 0^2)
distance_P = sqrt(9)
distance_P = 3
Now, we can compare the distances between point A, point P, and the center of the circle. The equation that verifies that point P lies on the circle C is the one that makes the distances equal.
Comparing the distances, we have:
distance_A = distance_P
3 = 3
Looking at the given answer choices, we can see that option b. (2+1)^2 + (-16+16)^2 = (2-2)^2 + (-16+13)^2 is the equation that verifies that point P(-1, -16) lies on circle C.
circle with centre (2,-16) is
(x-2)^2 + (y+16)^2 = r^2
but A(2,−13) lies on it, so
0^2 + 3^2 = r^2 = 9
equation : (x - 2)^2 + (y + 16)^2 = 9
so to see if P(−1,−16) lies on it, I would try to show LS = RS
LS = (-1 - 2)^2 + (-16+16)^2
= 9 + 0 = 9
= RS , then yes, point P lies on the circle
Don't understand why they would want to make it look so complicated