Answer:
The coordinates of T are (-1,4)
Step-by-step explanation:
The given coordinates of R and S are R(-5,12) and S(4, -6).
The point T divides RS in the ratio 4 : 5.
Let the coordinates of T = (x,y)
Now, by SECTION FORMULA:
If, m1 : m2 is the given ratio, then
[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]
So, here: [tex](x,y) = (\frac{4(4) + 5(-5)}{4+5} ,\frac{4(-6) + 5(12)}{4+5})[/tex]
or, [tex](x,y) = (\frac{16 -25}{9} ,\frac{-24+60}{9} ) \implies (x,y) = (\frac{-9}{9} \frac{36}{9} )[/tex]
or, (x, y) = (-1,4)
Hence, the coordinates of T are (-1,4)
