1.find the distance between the points (-1,2) and (3,4).express your answer in simplest radical form.

Question

3.a circle with center C(4,-2) passes through the point A(1,3).does the point B(8,-2) lie inside the circle?prove your answer.

Answer 1

1.
change in x = 4
change in y = 2
so
hypotenuse = sqrt (16 + 4) = sqrt (20) = sqrt(2*2*5) = 2 sqrt 5

Answer 2

How far is A from the center? (see last problem for how to calculate distance from C to A)
then
How far is B from the center ? ( same deal)
if B is further from the center than A, then B is outside the circle.

Answer 3

the radius is ...√[(3 - -2)^2 + (1 - 4)^2]

the distance to B is ... 8 - 4