Question

The coordinates of the endpoints of QR are Q(4,18) and R(16,6). Point S is on QR and divides it such that QS:RS is 3:1. The coordinates of point S are:

A. (7, 15)
B. (10, 12)
C. (12, 9)
D. (13, 7)

Answer 1

The coordinates of point S on QR are (13,9).

Step-by-step explanation:

To find the coordinates of point S on QR, we need to calculate the coordinates using the ratio QS:RS = 3:1.

Let's first find the distance between Q and R:

d = sqrt((16-4)^2 + (6-18)^2) = sqrt(144 + 144) = sqrt(288) = 12sqrt(2).

Then, we can find the distance between Q and S:

QS = (3/4) * d = (3/4) * 12sqrt(2) = 9sqrt(2).

Next, we can find the distance between R and S:

RS = (1/4) * d = (1/4) * 12sqrt(2) = 3sqrt(2).

Since Q is at (4,18), we can find the x-coordinate of S by subtracting the x-coordinate of Q from the x-coordinate of R multiplied by the ratio QS:RS:

x-coordinate of S = 4 + (16-4) * (3/4) = 4 + 12 * (3/4) = 4 + 9 = 13.

Similarly, we can find the y-coordinate of S by subtracting the y-coordinate of Q from the y-coordinate of R multiplied by the ratio QS:RS:

y-coordinate of S = 18 + (6-18) * (3/4) = 18 - 12 * (3/4) = 18 - 9 = 9.

Therefore, the coordinates of point S are (13,9).