Theory question 102
Coordinate Geometry(a) Find the coordinates of the point which divides the line joining (7, −5) and (−2, 7) externally in the ratio 3 : 2.
(b) Without using calculators or mathematical tables, evaluate 2/(1 − √2) − 2/(2 + √2), leaving the answer in the form p + q√n, where p, q and n are integers.
Show the model answer
Model answer
(a) External division: ((3(−2) − 2(7))/(3 − 2), (3(7) − 2(−5))/(3 − 2)) = (−20, 31).
(b) 2/(1 − √2) = −2 − 2√2; 2/(2 + √2) = 2 − √2.
Difference = −2 − 2√2 − 2 + √2 = −4 − √2 (p = −4, q = −1, n = 2).
Explanation
For external division use (mx₂ − nx₁)/(m − n).