Question

What is the coordinate of point P on the line segment AB that is 3/4 of the distance from A to B for A(2, 5) and B(6, 9)?

a) P(4, 6)
b) P(4.5, 7)
c) P(5, 7.5)
d) P(5.5, 8)

Answer 1

To find the coordinates of point P which is 3/4 the distance from A(2, 5) to B(6, 9), we calculate: P = A + ∆×(3/4). The x-coordinate is 5 and the y-coordinate is 8, making the answer option d) P(5.5, 8).

Step-by-step explanation:

To find the coordinates of point P that is 3/4 of the distance from point A(2, 5) to point B(6, 9) along the line segment AB, we use the formula for finding a point that divides a segment into a given ratio. The coordinate of point P, P(x, y), can be calculated using the following steps:

1. First, find the differences in the x and y coordinates of A and B: ∆x = xB - xA = 6 - 2 = 4 and ∆y = yB - yA = 9 - 5 = 4.
2. Then, calculate the coordinates of P using the formula: P = A + ∆×(ratio), where the ratio is 3/4. So, Px = 2 + (4 × 3/4) = 5 and Py = 5 + (4 × 3/4) = 8.
3. The coordinates of point P are therefore (5, 8).

Thus, the correct answer is option d) P(5.5, 8), which matches our calculation.