Answer: D) reflection across y = -x
Explanation:
When we reflect over y = x, we basically swap x and y. So for instance, the point (3,1) becomes (1,3).
When reflecting over y = -x, we will do the same thing but we'll make each coordinate swap in sign from positive to negative (or vice versa). The rule for reflecting over y = -x is
So if we apply that rule to point A(3,1) then it becomes A ' (-1, -3).
Similarly, B(1,5) moves to B ' (-5, -1)
Finally, C(6,9) becomes C ' (-9, -6)
we know that in direct variation as x increase y also increases.
in indirect variation x decreases y increase and vice versa.
in part a we have x at top (numerator ) and y at denominator it mean indirect variation (as x increases y decreases).
to find k we know that for indirect variation xy=k
if we rewrite the equation x=9/y we get xy=9
which mean k=9 .
in part b we have 4xy=20 if we simplify this equation we get
so here if we rewrite in terms of x.
we get x=5/y which represents indirect variation.
and we know xy=k
we have xy=5 .so k=5