Question

P lies on a line segment AB, and AP = 3/4AB. A is at (5, 4), and B is at (-3, -2). Find the coordinates of P.

a) (-1, 0)
b) (1, 2)
c) (2, 1)
d) (0, -1)

Answer 1

The coordinates of point P on line segment AB with AP = 3/4 AB and coordinates A(5, 4) and B(-3, -2) are calculated as (-1, 1/2). This does not match any of the provided options. Therefore, none of the options a), b), c), or d) are correct.

Step-by-step explanation:

To find the coordinates of point P that lies on the segment AB such that AP = 3/4 AB, we can use the concept of partitional ratios in coordinate geometry. The coordinates of point A are (5, 4), and point B are (-3, -2).

Using the formula for a point that divides a segment in a given ratio, the coordinates of point P can be calculated as:

• x-coordinate of P = [(1 - ratio) * x-coordinate of A + (ratio) * x-coordinate of B] / (1)
• y-coordinate of P = [(1 - ratio) * y-coordinate of A + (ratio) * y-coordinate of B] / (1)

Substituting the values we have ratio = 3/4, x-coordinate of A = 5, y-coordinate of A = 4, x-coordinate of B = -3, and y-coordinate of B = -2:

• x-coordinate of P = [(1 - 3/4) * 5 + (3/4) * -3] / 1 = (5/4 + (-9/4)) / 1 = -1
• y-coordinate of P = [(1 - 3/4) * 4 + (3/4) * -2] / 1 = (4/4 - 3/2) / 1 = 1/2

However, none of the provided choices (-1, 0), (1, 2), (2, 1), (0, -1) have the calculated coordinates (-1, 1/2). Therefore, none of the options a), b), c), or d) match the calculations for point P.