Question

The endpoints of RS are R(–5, 12) and S(4, –6). What are the coordinates of point T, which divides RS into a 4:5 ratio?

(4, –1)
(–1, 4)
(2.2, –2.4)
(–2.4, 2.2)

Answer 1

B. (-1,4) is your answer (got it right on e2020)

Answer 2

Option 2 is correct that is (-1,4)

Explanation:

We will use the section formula to find the coordinates of T

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

Here,
`m_1=4,m_2=5,x_1=-5,y_1=12,x_2=4,y_2=-6`

On substituting the values in the formula we get

`(x,y)=(4\cdot 4+5\cdot -5)/(4+5),(4\cdot -6+5\cdot 12)/(4+5)`

`\Rightarrow (x,y)=(4\cdot 4+5\cdot -5)/(4+5),(4\cdot -6+5\cdot 12)/(4+5)`

`\Rightarrow (x,y)=(16-25)/(9),(-24+60)/(9)`

`\Rightarrow (x,y)=(-9)/(9),(36)/(9)`

`\Rightarrow (x,y)=(-1,4)`

Therefore, option 2 is correct that is (-1,4)