Question

The coordinates of the endpoints of OP are O(-7,3) and P(2,21). Point Q is on OP and divides it such that OQ:PQ is 7:1. What are the coordinates of Q?

a) (0,15)

b) (-1,11)

c) (1,9)

d) (3,7)

Answer 1

To find the coordinates of point Q, calculate the distance between points O and P, and then divide the distance OQ by 8. Finally, use the midpoint formula to find the coordinates of Q.

Step-by-step explanation:

To find the coordinates of point Q, we first need to find the distance between points O and P. Using the distance formula, we can calculate that the distance between O and P is:

d = sqrt((2 - (-7))^2 + (21 - 3)^2)

= sqrt(9^2 + 18^2)

= sqrt(81 + 324)

= sqrt(405)

= 9sqrt(5)

Since OQ:PQ is given as 7:1, we can find the distance OQ by dividing the total distance, 9sqrt(5), by 8 (7+1).

OQ = (7/8) * 9sqrt(5)

= (63/8)sqrt(5).

Using the midpoint formula, we find the x-coordinate of Q by taking the average of the x-coordinates of O and P:

x-coordinate of Q = (-7 + 2)/2

= -5/2.

Similarly, we find the y-coordinate of Q by taking the average of the y-coordinates of O and P:

y-coordinate of Q = (3 + 21)/2

= 24/2

= 12.

Therefore, the coordinates of point Q are (-5/2, 12).