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

Answer:

(2,-1)

Step-by-step explanation:

Answer 2

Answer: D. (2,-1)

Step-by-step 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

$x\ coordinate=\frac{mx_2+nx_1}{m+n}$

$y\ coordinate=\frac{my_2+ny_1}{m+n}$

Using section formula, we have

The y coordinate of D =$\frac{5(2)+3(-6)}{5+3}=\frac{10-18}{8}=\frac{-8}{8}=-1$

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