Question

6. AB has coordinates A(-5,9) and B(7,-7). Points P, Q, and T are collinear
points 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 that
partitions AB into a ratio of 3:2?
А) AP
B) PQ
C) QT
D) TB

Answer 1

Answer:

C) QT

Step-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

$x=\frac{mx_2+nx_1}{m+n}$

and

$y=\frac{my_2+ny_1}{m+n}$

We plug in the coordinates of A(-5,9) and B(7,-7) and m=3, n=2 to get:

$x=\frac{3*7+2*-5}{3+2}$

$x=\frac{21-10}{5}$

$x=\frac{11}{5}$

and

$y=\frac{3*-7+2*9}{3+2}$

$y=\frac{-21+18}{5}$

$y=-\frac{3}{5}$

C has coordinates  $(\frac{11}{5},-\frac{3}{5})$

The line segment that contains C is $QT$

See attachment.