You should know that you can predict changes in coordinates after translations without a graph or anything like that.
(x, y) reflected over the x axis = (x, -y) (x, y) reflected over the y axis = (-x, y) (x, y) rotated 90 degrees around the origin = (y, -x) (x, y) rotated 180 degrees around the origin = (-x, -y) (x, y) rotated 270 degrees around the origin - (-x, y)
So here's our set of points. A(1, 2), B(4, 6), C(4, 6)
Here's those points reflected over the x axis. A'(1, -2), B'(4, -6), C'(4, -6)
And here's <em>those</em> points rotated 180° around the origin. A''(2, -1), B''(6, -4), C''(6, -4)
I think you made a mistake writing down the question, though, because B and C are the same yet you say ABC forms a triangle. You should be able to go through this process with whatever the coordinate was supposed to be.
The given is that A B C D <span>x 4 = D C B A </span><span> Possible values of A are 1 or 2. It can't be 1 since the </span><span> </span><span>final result A is in unit place and 1 is not possible when we multiply any number by 4 </span><span> 2 B C D x </span><span>4 = </span><span>D C B 2</span> It is clear above, that D = 8 2 B C 8 x <span>4 = </span><span>8 C B 2</span> Possible values of B should be 1 or 2 We try B=1
2 1 C 8 x <span>4 = </span><span>8 C 1 2
</span>To find for C, you can use the equation:
(2000+100+10C+8) x 4 = 8000+100C+10+240C = 432-12 = 420 Therefore,