Math Functions 11/12 Help please.

Heyy, stuck on this question:

Consider the relation between x and y that consists of all points
such that the distance from to the origin is 5.
a) Is (4, 3) in the relation? Explain.
b) Is (1, 5) in the relation? Explain.
c) Is the relation a function? Explain.

WHAT THE HELL DO I DO!?

Like, I don't get the question.

Please help me, thanks.

the distance from to the origin is 5.

sounds like a circle

the easy points to work with are
(0,5)
(0,-5)
(5,0)
(-5,0)

neither of your points are 5 from the origin

and no, it is not a function

They're basically asking that if you have x and y coordinates, are they 5-units away from the origin?

If you plot the points given on a graph, you will need to figure out how far they are from the point of origin, the center of the graph. That you will need to use either trigonometry (sine, cosine) or the Pythagorean Theorem.

If the point is 5-units away, then it is a part of the function. If it is not 5-units away from the origin, then it is not a party of the function.

This is probably the simplest way I could try to explain without actually drawing it.

If did not recognize that the information gave you a circle with the center at the origin and a radius of 5.

we can use the distance formula to find the distance from one point to another

d = sqrt((x - x)^2 + (y - y)^2)
d = sqrt((4 - 0)^2 + (3 - 0)^2)
d = sqrt(16 + 9)
d = sqrt(25) = 5 so this point is on the circle

d = sqrt((1 - 0)^2 + (5 - 0)^2)
d = sqrt(1^2 + 5^2)
d = sqrt(26) > sqrt(25) so not on circle

no because you can get different y values for each x value

d^2 = 4^2 + 3^2
d^2 = 16 + 9 = 25
d = 5
a) yes
b) no
c)no