Question

QR has endpoints Q(1,3) and R(8,10). Point S divides QR into two parts with lengths in a ratio of 2:1. What are the two possible locations of S?

a) S(3,6) and S(6,8)
b) S(2,4) and S(5,7)
c) S(4,7) and S(7,9)
d) S(1,2) and S(7,10)

Answer 1

To find the two possible locations of point S, divide the line segment QR into two parts with a ratio of 2:1. Use the differences in the x and y-coordinates of Q and R to determine the locations of S.

Step-by-step explanation:

To find the possible locations of point S, we need to divide the line segment QR into two parts in a ratio of 2:1. First, we find the difference in the x-coordinates of Q and R, which is 8 - 1 = 7. Then, we find the difference in the y-coordinates of Q and R, which is 10 - 3 = 7.

To divide QR into two parts with a ratio of 2:1, we multiply the differences in the x and y-coordinates by 2/3. Then, we add the products to the x-coordinate of Q and the y-coordinate of Q to find the possible locations of S.

Using this method, we find that the two possible locations of S are S(3,6) and S(6,8).