Answer:
Option 2 is correct that is (-1,4)
Step-by-step explanation:
We will use the section formula to find the coordinates of T
Formula is [tex](x,y)=\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Here, [tex]m_1=4,m_2=5,x_1=-5,y_1=12,x_2=4,y_2=-6[/tex]
On substituting the values in the formula we get
[tex](x,y)=\frac{4\cdot 4+5\cdot -5}{4+5},\frac{4\cdot -6+5\cdot 12}{4+5}[/tex]
[tex]\Rightarrow (x,y)=\frac{4\cdot 4+5\cdot -5}{4+5},\frac{4\cdot -6+5\cdot 12}{4+5}[/tex]
[tex]\Rightarrow (x,y)=\frac{16-25}{9},\frac{-24+60}{9}[/tex]
[tex]\Rightarrow (x,y)=\frac{-9}{9},\frac{36}{9}[/tex]
[tex]\Rightarrow (x,y)=(-1,4)[/tex]
Therefore, option 2 is correct that is (-1,4)
