Question

A directed segment QR¯¯¯¯¯ with endpoints at Q (2, 1) and R (8, 13) is partitioned from Q to R into a 1:2 ratio at point Z. What are the coordinates of Z?

(2, 4)


(4, 5)


(6, 9)


(9, 10)

Answer 1

The coordinate of the point Z is (4, 5)

Explanation:

The given information are;

The coordinates of the endpoints of the directed segment QR are Q(2, 1) and R(8, 13)

The ratio of the partition of the directed line segment QR from Q to R = 1:2

The location of the point at the directed line segment is partitioned = Point Z

Therefore, we have;

The proportion of the partition segment QZ to QR is given as follows;

QZ = 1/(1 + 2) × QR = 1/3·QR

ZR = 2/(1 + 2) × QR = 2/3·QR

Which gives the coordinate of the point Z as follows;

The coordinate of the point Z = (2 + (8 - 2)×1/3, 1 + (13 - 1)×1/3)

The coordinate of the point Z = (2 + 2, 1 + 4) = (4, 5)

The coordinate of the point Z = (4, 5).