Question

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)

Answer 1

Option A

Explanation:

A. (2, -1)

Answer 2

A.

`Point\ C = (2,-1)`

Explanation:

Given

`A = (2,-6)`

`B = (10,2)`

`m:n = 5:3`

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;

`D(x,y) = ((mx_2 + nx_1)/(m+n),(my_2 + ny_1)/(m+n))`

Where

`(x_1,y_1) = (2,6)`

`(x_2,y_2) = (10,2)`

`m:n = 5:3`

`D(x,y) = ((5 * 10 + 3 * 2)/(5+3),(5 * 2 + 3 * -6)/(5+3))`

`D(x,y) = ((50 + 6)/(8),(10 - 18)/(8))`

`D(x,y) = ((56)/(8),(-8)/(8))`

`D(x,y) = (7},-1)`

Since AC is vertical

Then, Point C has the same x coordinate as A

`x-coordinate = 2`

Similarly;

Since CD is horizontal

Then, Point C has the same y coordinate as D

`y-coordinate = -1`

Hence,

`Point\ C = (2,-1)`