A certain game is played on a board that shows a portion of the xy-coordinate plane. During one move in the game, a marker at a point (a, b) is first moved to the point (b, a) and then moved 3 units to the left. During such a move, a marker that is at (4,3) will be moved to

(0,4)

Step-by-step explanation:

Given: During one move in the game, a marker at a point (a,b) is first moved to the point (b,a) .                                                                     (i)

And then moved 3 units to the left.                                   (ii)

Translation rule to move a point (x,y) c units left : (x,y)→(x-c,y)

Now, (4,3)  first will become (3,4)  [using (i)]

Then, (3,4)→(3-3,4)=(0,4)   [using (ii) and translation rule]

Hence, During such a move, a marker that is at (4,3) will be moved to (0,4).

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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