Question

Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

A) (-1, 3)
B) (0, 4)
C) (1, 5)
D) (2, 6)

Answer 1

To find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio, we use the section formula. We substitute the given ratio into the formula and solve for the coordinates. For option D, the coordinates of point P are (2, 4).

Step-by-step explanation:

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

Let the coordinates of point P be (x, y).

Using the section formula, we have:

x = (APx * k + PBx)/(k + 1)

y = (APy * k + PBy)/(k + 1)

Using the given ratio, we can substitute the values and solve for (x, y).

For example, if k = 2, we can substitute the values of APx, APy, PBx, and PBy into the formulas to find the coordinates of point P.

Substituting the values from option D:

x = (2 * 2 + 3)/(2 + 1) = 2

y = (6 * 2 + 0.75)/(2 + 1) = 4

So, the coordinates of point P for option D are (2, 4).