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. (5, -3) B. (2, -3) C. (7, -1) D. (2, -1)

Answer 1

(2,-1)

Explanation:

Answer 2

Answer: D. (2,-1)

Explanation:

Given: In the diagram, point D divides line segment AB in the ratio of 5:3.

Since, line segment AC is vertical then the x coordinate of C will be same as A (2) and line segment CD is horizontal then the y coordinate of C will be same as D.

Coordinates of A = (2,-6)

Coordinates of B = (10,2)

Section formula: If a point P(x,y) divides a line segment MN with in ration m:n, then

`x\ coordinate=(mx_2+nx_1)/(m+n)`

`y\ coordinate=(my_2+ny_1)/(m+n)`

Using section formula, we have

The y coordinate of D =
`(5(2)+3(-6))/(5+3)=(10-18)/(8)=(-8)/(8)=-1`

Thus, the coordinates of C =(2,-1)