Question

Please help me answer this. I think that for the first one the answer is A, but I am not sure. There are two parts to the question.

Answer 1

P=(5,4). Q=(7,3). R=(8,6) AND S=(4,1)

PQ = (7-5 , 3-4) =PQ=(2,-1)

RS =(4-8 , 1-6) =RS=(-4 , -5). 4.RS=(-16 , -20)

PQ+4RS = (-16-2 , -19) ; PQ = (-18 , -19)

Answer 2

Vector $PQ=(7-5, 3-4)=(2, -1)$.  $4RS=4 \cdot (4-8, 1-6) = 4 \cdot (-4, -5) = (-16, -20)$.  So the sum is $(-14, -21)$.

For the second, the magnitude is the square root of the sum of the squares of the components.  This is equal to $\sqrt{(-14)^2+(-21)^2} = \sqrt{637}=7\sqrt{13}$.