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

Answer:

d.(4,-0.5)

Step-by-step 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:

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

Using the formula

The coordinate of point C are

$x=\frac{3(7)+1(-5)}{3+1},y=\frac{3(-2)+1(4)}{3+1}$

$x=\frac{16}{4},y=\frac{-1}{2}$

$x=4,y=-0.5$

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

Option d is true.