Sat question: a circle in the xy-plane has a diameter with endpoints (-1,-3) and (7,3). if the point (0,b) lies on the circle and b > 0, what is the value of b

1) use the distance formula to find that the radius (r) of the circle = 5

2) use the midpoint formula to find that the center of the circle (h,k) = (3, 0)

3) Now use the formula of a circle and input the (h,k) and r to create:

(x - 3)² + (y - 0)² = 5² → (x - 3)² + y² = 25

4) input the "x" value given in the question (x = 0) and solve for "y":

(0 - 3)² + y² = 25 → 9 + y² = 25 → y² = 16 → y = +/- 4

Since the question states that "b" must be positive, you can disregard the -4.

b = 4

step-by-step explanation:

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3