Question

Find the coordinates of point p along the directed line segment ab so that the ratio of ap to pb is 4 to 1. Given that a(1,3) and b(8,4), what are the coordinates of point p?

Answer 1

To find the coordinates of point P along the directed line segment AB, use the midpoint formula to find the coordinates of the midpoint M. Then, use the given ratio of AP to PB to divide the line segment AM and MB and find the coordinates of point P.

Step-by-step explanation:

To find the coordinates of point P along the directed line segment AB, we can use the concept of midpoint and the given ratio of AP to PB.

First, let's find the coordinates of the midpoint M of AB using the midpoint formula:

M = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the values, we get:

M = ((1 + 8)/2, (3 + 4)/2) = (4.5, 3.5)

Next, we can find the coordinates of point P by dividing the line segment AM and MB in the ratio of 4 to 1:

P = ((4 * x2 + 1 * x1)/5, (4 * y2 + 1 * y1)/5)

Substituting the values, we get:

P = ((4 * 8 + 1 * 1)/5, (4 * 4 + 1 * 3)/5) = (6.6, 3.5)