) Find the distance between A(2,3) and the midpoint of the join of B(4,5) and C(6,9).
b)i)Find the number of the different selections of 3 letters that can be made from the letters of the word SUCCESSFUL
ii)How many of these selections contain at least one vowel?
A(2, 3), B(4, 5), (X, Y), C(6, 9).
6 - 4 = 2(X - 4),
2 = 2X - 8
2x = 8 + 2 = 10,
X = 5.
9 - 5 = 2(Y - 5),
4 = 2Y - 10,
2Y = 10 + 4 = 14,
Y = 7.
d^2 = (X - 2)^2 + (Y - 3)^2,
d^2 = (5 - 2)^2 + (7 - 3)^2,
d^2 = 9 + 16 = 25,
d = 5.