Question

A is (3, 2) and point B is 4 units from A in the direction (1,-1)
Find AB(arrow).
Find the coordinates of B.

I can't do this question, Ive attempted it many times.

Answer 1

Since |B| = 4, B = <4/√2,-4/√2> = <2√2,-2√2>

AB = B-A = (2√2-3,-2√2-2)

Answer 2

I don't understand how you know that the modulus of B is 4

Answer 3

This answer isn't all too clear
AB = 4 divided by |(1, -1)| times (1, -1)
AB = 4/√2 times (1, -1)
AB = (4/√2, -4/√2) = (2√2, -2√2)

Next is Finding OB
OB = OA + AB
OB = (3,2) + (2√2, -2√2)
OB = (3 + 2√2, 2 - 2√2)

Now we can deduce the point B to be at
(3 + 2√2, 2 - 2√2)