Question

Here is a sketch of line L.

The points P(-6,0) and Q(0,3) are points on the line L
The Point R such that PQR is a straight line and PQ:QR = 2:3

Find the coordinates of R

Answer 1

Since the points P(-6,0) and Q(0,3) are points on the line L, the coordinates of R are (9, 7.5).

In this scenario, line ratio would be used to determine the coordinates of the point R on the directed line segment PR that partitions the segment into a ratio of 2 to 3.

In Mathematics and EuclideanGeometry, line ratio can be used to determine the coordinates of a point and this is modeled by this mathematical equation:

`M(x, y) = ((mx_2 + nx_1)/(m + n), (my_2 + ny_1)/(m + n))\\\\(0,3) = ((2x_2 + 3(-6))/(2 + 3), (2y_2 + 3(0))/(2 + 3))\\\\(0,3) = ((2x_2 -18)/(5), (2y_2 )/(5))\\\\\\\\0 = (2x_2 -18)/(5)\\\\2x_2 =18\\\\x_2=(18)/(2) \\\\x_2=9\\\\\\\\3=(2y_2 )/(5)\\\\y_2=(15)/(2) \\\\y_2=7.5`

Therefore, the coordinates of R are (9, 7.5).