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

Answer 1

D.(2, -1)

Explanation:

As you can see you only need to calculate the Y of the point C since the X can be reasoned out from the fact that it is a vertical line that goes up from point A which is located on (2,-6), so point C will be in x=2 as well, now we jsut have to calculate where is located on the Y point D, since point C and D are horizontally placed on the same line, they will share value for Y.

If AB= (2-(-6) = (2+6)=8, and AB is divided by point D in a ratio of 5:3, this means that from A to D on the Y vector there are 5 units of difference so you just add them up: -6+5=-1, and you´ve found the Y.

So the point C is located in (2,-1).

Answer 2

D

Explanation:

First, find the coordinates of pointD if A(2,-6), B(10,2) and point D divides line segment AB in the ratio of 5:3.

If point D divides the segment AB in the ratio m:n, then

`D\left((nx_A+mx_B)/(m+n),(ny_A+my_B)/(m+n)\right)`

So

`D\left((3\cdot 2+5\cdot 10)/(5+3),(3\cdot (-6)+5\cdot 2B)/(5+3)\right)=D(7,-1)`

Point C has the x-coordinate the same as point A and the y-coordinate the same as point D.

Thus, C(2,-1)