Question

In the coordinate plane, point C lies on segment AB. If the ratio of the length of segment AC to the length of segment CB is 3:1, find the x-coordinate of C given the coordinates of A(3, 12) and B (14, 17).

Question 14 options:


A. 11.25



B. 6



C. 5.75



D. 12

Answer 1

A. 11.25

Explanation:

If point C(x, y) divides line segment AB with end points at A(
`x_1,y_1`) and B(
`x_2,y_2\\`) in the ratio on n:m, then the coordinates of point C is:

`x=(n)/(n+m)(x_2-x_1)+x_1 \\\\y=(n)/(n+m)(y_2-y_1)+y_1`

Given that segment AB is divided by point C in the ratio of 3:1. Given A(3, 12) and B (14, 17). Let coordinate of C be (x, y), hence:

`x=(n)/(n+m)(x_2-x_1)+x_1\\\\x=(3)/(3+1)(14-3)+3=(3)/(4)(11)+3=11.25 \\\\\\y=(n)/(n+m)(y_2-y_1)+y_1\\\\y=(3)/(3+1)(17-12)+12=(3)/(4)(5)+12=15.75`

Therefore, the coordinate of point C = (11.25, 15.75)

The x coordinate of point C is 11.25