How to find the transformations (matrix)?

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Answer 1 · 2018-05-24T21:28:05

Part i.

Given:

$T_2([(x),(y)]) = [(1,0),(0,-1)][(x),(y)] +[(1),(3)]$

Written point form:

$(x_(T_2),y_(T_2)) = (x+1,3-y) larr$ answer to part i.

Part ii.

# T_3([(x),(y)])=-T_2([(x),(y)])

$T_3 = -([(1,0),(0,-1)][(x),(y)] +[(1),(3)])$

$T_3 = [(-1,0),(0,1)][(x),(y)] +[(-1),(-3)]$

In point form:

#(x_(T_3),y_(T_3)) = (-1-x,y-3)

Substitute $(x,y) = (1,1)$

$(x_(T_3),y_(T_3)) = (-1-1,1-3)$

$(x_(T_3),y_(T_3)) = (-2,-2) larr$ answer to part ii.