Question

Find the coordinates of P so that P
partitions AB in the ratio 5:1 with A (2, 4) and B (8, 10).

Answer 1

The coordinates of point P that partitions the line segment AB in the ratio 5:1 where A is (2,4) and B is (8,10) are (7, 9).

Step-by-step explanation:

To find the coordinates of point P that partitions the line segment AB in the ratio 5:1 where A (2,4) and B (8,10), we use the section formula, which is given for partitions in the ratio m:n by the following:

Point P (x, y) = ((mx2 + nx1) / (m+n), (my2 + ny1) / (m+n))

In our case, ratio m:n is 5:1, point A has coordinates (2,4), and point B has coordinates (8,10). Applying the section formula, we get:

P (x, y) = ((5*8 + 1*2) / (5+1), (5*10 + 1*4) / (5+1))

P (x, y) = ((40 + 2) / 6, (50 + 4) / 6)

P (x, y) = (42 / 6, 54 / 6)

P (x, y) = (7, 9)

So, the coordinates of point P are (7, 9).