Question

Emily draws point C on the line segment so that the ratio of AC to CB is 3 to 1. What are the coordinates of Point C?

a. (-2,2.5)

b.(-1,2)

c.(3,0)

d.(4,-0.5)​

Answer 1

d.(4,-0.5)

Explanation:

We are given that the ratio of AC to CB

AC:CB=3:1

`m_1=3,m_2=1`

From given figure

The coordinates of A are (-5,4)

The coordinates of B are (7,-2)

We have to find the coordinates of C

Section formula:

`x=(m_1x_2+m_2x_1)/(m_1+m_2),y=(m_1y_2+m_2y_1)/(m_1+m_2)`

Using the formula

The coordinate of point C are

`x=(3(7)+1(-5))/(3+1),y=(3(-2)+1(4))/(3+1)`

`x=(16)/(4),y=(-1)/(2)`

`x=4,y=-0.5`

Hence, the coordinate of point C are (4,-0.5)

Option d is true.