Question

The coordinates of the endpoints of OP are O(–12,8) and P(0,–4). Point Q is on OP and divides it such that OQ:PQ is 1:3. What are the coordinates of point Q?

a) Q(-10,6)

b) Q(-8,4)

c) Q(-6,2)

d) Q(-4,0)

Answer 1

If the ratio of OQ:PQ is 1:3, then the coordinates of point Q can be found using the section formula.

Step-by-step explanation:

To find the coordinates of point Q, we can use the concept of section formula. Since the ratio of OQ:PQ is 1:3, we can divide the distance between the x-coordinates and y-coordinates of O and P in the same ratio.

x-coordinate of Q = (1/4)*(0) + (3/4)*(-12) = -9

y-coordinate of Q = (1/4)*(-4) + (3/4)*(8) = 6

Therefore, the coordinates of point Q are (-9,6). So, the correct answer is option a) Q(-10,6).