Question

The endpoints of the directed line segment AB are A(4,1) and B(8, 7). Find the coordinates of point P along AB so that the ratio of AP to PB is 3 to 1.

a) P(5, 5)
b) P(6, 6)
c) P(7, 7)
d) P(8, 8)

Answer 1

To find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is 3 to 1, you can use the section formula. The coordinates of point P are (6, 2).

Step-by-step explanation:

To find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is 3 to 1, we can use the section formula.

The section formula states that if A(x1, y1) and B(x2, y2) are the endpoints of a line segment, and P(x, y) divides the line segment in the ratio m:n, then the coordinates of P can be found using the formula:

x = (nx2 + mx1)/(m + n) and y = (ny2 + my1)/(m + n).

Using this formula, we can plug in the values: x1 = 4, y1 = 1, x2 = 8, y2 = 7, m = 3, and n = 1.

x = (1 * 8 + 3 * 4)/(3 + 1) = 6 and y = (1 * 7 + 3 * 1)/(3 + 1) = 2.

Therefore, the coordinates of point P are (6, 2).