What is the distance from the origin of point a graphed on the complex plane below?
a. square root of 5
b. square root of 13
c. 9
d. 13

Coordinates of point A are
(-3,-2)

Origin lies in the center of coordinate system. That means that you can picture this as right triangle with sides 3 and 2 and you need to find hypotenuse of it.

Using pythagoras theorem we calculate:
h^2 = 3^2 + 2^2 = 13
h = sqrt 13

Answer is b

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12