If the vertices of triangle qrs have coordinates q(1, −2), r(3, −2), and s(2, −4), which coordinates are the coordinates of the vertices of triangle qꞌrꞌsꞌ when triangle qrs is reflected across the x-axis?
a. qꞌ(−1, −2), rꞌ(−3, −2), sꞌ(−2, −4)
b. qꞌ(1, 2), rꞌ(3, 2), sꞌ(2, 4)
c. qꞌ(2, 1), rꞌ(2, 3), sꞌ(4, 2)
d. qꞌ(2, −4), rꞌ(6, −4), sꞌ(4, −8)

B
The value of x does not change in reflection across the x axis while the sign of the value of y is reversed because it travels a distance equal to its distance from the x-axis in the negative y-axis.

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

He was paid 23 dollars for each lawn