Question

The coordinates of the endpoints of PQ are P(3,5) and Q(18,14). Point R is on PQ and divides it such that PR:QR is 1:2. Are the coordinates of R?

a) (8, 11)
b) (10, 12)
c) (12, 13)
d) (14, 14)

Answer 1

To find the coordinates of point R on the line segment PQ, we can use the midpoint formula and divide the distance between P and Q by the given ratio. The coordinates of R are approximately (7, 6.33...), and the closest option is (8, 11).

So option (A) is the correct answer.

Step-by-step explanation:

To find the coordinates of point R, we first calculate the distance between points P and Q by using the distance formula: √((x2 - x1)^2 + (y2 - y1)^2). Plugging in the given coordinates, we get √((18 - 3)^2 + (14 - 5)^2) = √(225 + 81) = √306.

Since PR: QR is 1:2, we can divide the distance between P and Q into three parts: 1/3 of √306 for PR and 2/3 of √306 for QR. A convenient way to do this is to use the midpoint formula: ((x1 + x2)/2, (y1 + y2)/2). Plugging in the values, we get ((3 + 18)/3, (5 + 14)/3) = (7, 6.33...).

Therefore, the coordinates of point R are approximately (7, 6.33...). Since none of the given options match exactly, the closest answer is (8, 11), option a).