:
δlʹmʹnʹ is a dilation of δlmn with the origin as the center of dilation.
the coordinates of the vertex of ∠lʹmʹnʹ are (6, 12).
if the scale factor is 3, what are the coordinates of the vertex of ∠lmn?

Since the origin is the center of the dilation, this means we simply multiply every coordinate of the given point by the scale factor.

(6,12) would turn into (18,36) since
6*3 = 18
12*3 = 36

The final answer is (18,36)

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

Bis the answer! hope this