Question

Find the coordinates of point B along a directed line segment from A(3,4) and C(3,9) so that the ratio o

to BC is 4:1.

Answer 1

Point B is (3, 8)

Explanation:

Hello, Jacky,

Note that points A and C have the same x-coordinate and thus lie on the same vertical line, which is x = 3. To determine the length of this directed line segment, we need only subtract 4 from 9, obtaining 5.

Now if we start at (3,4), move up 4 units along this vertical line, plot a point there, and finally move 1 more unit along this line to C(3, 9), we will have partitioned the line in the ratio 4:1. To find the coordinates of this point, we simply take x = 3 (see above) and add 4 to y = 4), obtaining the point (3, 8). This is Point B.

Point B is (3, 8)