The information given is sufficient for this proof .
Slope of a line passing through x1 ,y1) and ( x2,y2) is given by the formula :
M = ( y2 - y1)/ ( x2-x1)
________________________________
Let us start finding the slope of line PQ
the given points are ( a,b) and ( c,d)
using the slope formula we get :
slope of line PQ = m= ( d-b) /( c-a)
Let us now try finidng slope of the another line P'Q'
It is passing through ( -b ,a) and (-d,c)
using the formula we get slope of P'Q' = m' = ( c-a) /( -d - -b)
m'= ( c-a) /( -d+b)
m'= ( c-a) / -( b-d Let us find the product of m and m' :
( d-b ) * ( c-a)
----------- ------------ = -1
(c-a) - ( b-d)
Because we got product of m and m' = -1 hence proved product of perpendicular lines are negative reciprocal of each other .
You can use the distance formula for this:
√(x2-x1)²+(y2-y1)²
so you'll get √(1-4)²+(11-7)² = √(-3)²+(4)² = √9+16 = √25 = 5 and 5 is your answer
(64)^3/2 = (sqrt(64))^3 = 8^3 = 512.
A way to remember what you have learned is creating notes or doing practice problems
