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

RT:TS = 4:5 so T divides RS internally with m = 4, n = 5. Use section formula:
T = ((n*x_R + m*x_S)/(m+n), (n*y_R + m*y_S)/(m+n))
= ((5·(−5) + 4·4)/9, (5·12 + 4·(−6))/9)
= ((−25+16)/9, (60−24)/9) = (−1, 4).

Answer: (−1, 4)