In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? A. (2, -1) B. (5, -3) C. (2, -3) D. (7, -1)

A.

Step-by-step explanation:

Given

Required

Determine the coordinates of C

Since, point D divides line AB in ratio, 5 : 3;

We start by calculating the coordinates of D;

This is done as follows;

Where

Since AC is vertical

Then, Point C has the same x coordinate as A

Similarly;

Since CD is horizontal

Then, Point C has the same y coordinate as D

Hence,

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x