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

C) QT

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=(mx_2+nx_1)/(m+n)`

and

`y=(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=(3*7+2*-5)/(3+2)`

`x=(21-10)/(5)`

`x=(11)/(5)`

and

`y=(3*-7+2*9)/(3+2)`

`y=(-21+18)/(5)`

`y=-(3)/(5)`

C has coordinates
`((11)/(5),-(3)/(5))`

The line segment that contains C is
`QT`

See attachment.