Question

Let AB be the directed line segment beginning at point A(2 , 4) and ending at point B(17 , 17). Find the point P on the line segment that partitions the line segment into the segments AP and PB at a ratio of 5:1. A. B. C. D.

Answer 1

To find the point that divides the line segment AB into the ratio 5:1, we can use the section formula. Plugging the given coordinates into the formula, we find that the coordinates of point P are (14, 11).

Step-by-step explanation:

To find the point that divides the line segment AB into the ratio 5:1, we can use the section formula. The section formula states that for a line segment AB with coordinates A(x1, y1) and B(x2, y2), the coordinates of a point P that divides AB in the ratio m:n are given by:

x = (mx2 + nx1) / (m + n)

y = (my2 + ny1) / (m + n)

For the given line segment AB, the coordinates of A are (2, 4) and the coordinates of B are (17, 17). Plugging these values into the section formula with the ratio 5:1, we get:

x = (5*17 + 1*2) / (5 + 1) = 14

y = (5*17 + 1*4) / (5 + 1) = 11

Therefore, the coordinates of point P are (14, 11).