Question

If p = (3, 5), then 2p, -4p and $\frac{1}{3}$ p are respectively (a, b), (c, d) and (e, 5/3). Find the value of -(a+b+c+d+e)

Answer 1

For p = (3, 5)
2p will be obtained by multiply x and y coordinates by 2.
i.e.,
$2p=\left(\right(3\times 2),(5\times 2\left)\right)$
$=(6,10)$
Similarly - $4p=\left(\right(3\times -4),(5\times -4\left)\right)=(-12,-20)\frac{1}{3}p=\left(\right(3\times \frac{1}{3}),(5\times \frac{1}{3}\left)\right)=(1,\frac{5}{3})$
So we get a = 6, b= 10, c = -12, d = -20, e = 1
=> a+b+c+d+e = 6+10-12-20+1
= -15
=> -(a+b+c+d+e) = 15