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

Answer:

Option (D)

Step-by-step 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 = $\frac{mx_2+nx_1}{m+n}$

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

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 = $\frac{3(6)+2(-4)}{3+2}$

  = $\frac{18-8}{5}$

h = 2

k = $\frac{3(1)+2(6)}{3+2}$

  = $\frac{3+12}{5}$

k = 3

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

Option (D) will be the answer.