AB has coordinates A(-5,9) and B(7,- 7). Points P, Q, and I 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?
Accepted Solution
A:
Answer:[tex]\overline{QT}[/tex]Step-by-step explanation:We want to find the coordinates of a certain point C(x,y) such that C divides [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] in the ratio m:n=3:2The x-coordinate is given by:[tex]x=\frac{mx_2+nx_1}{m+n}[/tex] The y-coordinate is given by:[tex]y=\frac{my_2+ny_1}{m+n}[/tex] AB has coordinates A(-5,9) and B(7,- 7)We substitute the values 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] Therefore C has coordinates [tex](\frac{11}{5},-\frac{3}{5})[/tex] The line segment that contains C is [tex]\overline{QT}[/tex]See attachment.