6. AB has coordinates A(-5,9) and B(7,-7). Points P, Q, and T are collinearpoints in AB with coordinates P(-2,5), Q(1, 1), and T(4, -3).Part A: Which of the following line segments would contain the point thatpartitions AB into a ratio of 3:2?А) APB) PQC) QTD) TB

Answer:C) QTStep-by-step explanation:We must first find the coordinates of C(x,y) which divides AB in the ration m:n=3:2.We use the formula[tex]x=\frac{mx_2+nx_1}{m+n}[/tex]and [tex]y=\frac{my_2+ny_1}{m+n}[/tex] We plug in the coordinates of A(-5,9) and B(7,-7) and m=3, n=2 to get:[tex]x=\frac{3*7+2*-5}{3+2}[/tex] [tex]x=\frac{21-10}{5}[/tex] [tex]x=\frac{11}{5}[/tex] and[tex]y=\frac{3*-7+2*9}{3+2}[/tex] [tex]y=\frac{-21+18}{5}[/tex] [tex]y=-\frac{3}{5}[/tex]C has coordinates  [tex](\frac{11}{5},-\frac{3}{5})[/tex] The line segment that contains C is [tex]QT[/tex]See attachment.