In the figure below, segment AB is the hypotenuse of right triangle ABC. Which of the following could be the coordinates of point C?

Answers A. (2,2) B. (0, 0) C. (2,1) D. (1,7)

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Polygon abcde is reflected to produce polygon a′b′c′d′e′. what is the equation for the line of reflection?

Emily is entering a bicycle race for charity. her mother pledges $0.90 for every 0.75 mile she bikes. if emily bikes 18 miles, how much will her mother donate?