Theory question 113
Binary Operations(a) The operation (*) is defined on the set of real numbers, R, by x(*)y = (x + y)/2, x, y ∈ R. (i) Evaluate 3(*)⅖. (ii) If 8(*)y = 8¼, find the value of y.
(b) In ΔABC, AB = (−4 / 6) and AC = (3 / −8). If P is the mid point of AB, express CP as a column.
Show the model answer
Model answer
(a)(i) 3(*)⅖ = (3 + ⅖)/2 = 17/10 = 1.7
(ii) (8 + y)/2 = 8¼ → 8 + y = 16½ → y = 8½
(b) AP = ½AB = (−2 / 3)
CP = CA + AP = −AC + AP = (−3 / 8) + (−2 / 3) = (−5 / 11)
Explanation
Go from C back to A and then along to P.