Question

Given the points A(-2,0) and B(5,3), find the x-coordinate of the point P on the directed line segment AB that partitions AB in the ratio 8:3. Round your answer to the nearest whole number.

A. 2
B. 1
C. 0
D. -1

Answer 1

The x-coordinate of the point P on the directed line segment AB that partitions AB in the ratio 8:3 is 1.

Step-by-step explanation:

To find the x-coordinate of point P that divides the line segment AB in the ratio 8:3, we'll use the section formula. The section formula for finding a point dividing a line segment with coordinates A(x1, y1) and B(x2, y2) in the ratio m:n internally is:

`\[x = \left((mx_2 + nx_1)/(m+n)\right)\]`

Given points A(-2,0) and B(5,3), the ratio 8:3 splits into 8/11 and 3/11 respectively.

Let's substitute the values into the formula to find the x-coordinate of point P:

`\[x = \left((3*5 + 8*(-2))/(3+8)\right)\]\[x = \left((15 - 16)/(11)\right)\]\[x = \left((-1)/(11)\right)\]`

Rounding this to the nearest whole number, the x-coordinate of point P is 0.