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?

Answer 1

Answer:

C(2,-1) that is option C is correct.

Step-by-step explanation:

We have been given the figure:

We will first find the coordinates og D.

Using section formula:

$(x,y)=\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}$

Here,$x_1=2,y_1=-6,x_2=10,y_2=2,m_1=5,m_2=3$

On substituting the values in the formula we get:

$(x,y)=\frac{5\cdot 10+3\cdot 2}{8},\frac{5\cdot 2+3\cdot -6}{8}$

On simplification we get:

$(x,y)=\frac{56}{8},\frac{-8}{8}$

So, coordinates of D are: (7,-1)

Now, we need to find the coordinates of C

We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line

And coordinate of y will be same as y in D since CD is horizontal line.

C(2,-1) option C is correct.