Question

Point Q lies on segment AB, where point A is located at (- 4, 6) and point B is located at (6, 1). If AQ: QB = 3:2, where is point on

the segment AB? Find the coordinates of point Q.
A (4,0)
B (3,2)
C (0,4)
D (2,3)

Answer 1

Option (D)

Explanation:

If a point (h, k) divides the line segment having ends at
`(x_1, y_1)` and
`(x_2,y_2)` in the ratio of m : n then,

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

k =
`(my_2+ny_1)/(m+n)`

If a point Q(h, k) divides the segment with ends A(-4, 6) and B(6, 1) in the ratio of 3 : 2 then,

h =
`(3(6)+2(-4))/(3+2)`

=
`(18-8)/(5)`

h = 2

k =
`(3(1)+2(6))/(3+2)`

=
`(3+12)/(5)`

k = 3

Therefore, Coordinates of the point Q are (2, 3).

Option (D) will be the answer.