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1) the initial coordinaes of the triangle are: ( 1,2 ), (3,1 ) and (3,4 ) so if it is translated 2 units left and 1 unit up we have to rest 2 to the x coordinate and add 1 to the y coordinate so:
[tex]\begin{gathered} (1,2)\to(-1,3) \\ (3,1)\to(1,2) \\ (3,4)\to(1,5) \end{gathered}[/tex]So I will graph the initial triangle in blue and the translated triangle in red so:
2) the initial rectangle has coordinates (-3,2) (3,5) (4,3) (-2,0) and we translate 1 unit right and 4 units down so:
[tex]\begin{gathered} (-3,2)\to(-2,-2) \\ (3,5)\to(4,1) \\ (4,3)\to(5,-1) \\ (-2,0)\to(-1,-4) \end{gathered}[/tex]So I will graph the initial rectangle in blue and the translated rectangle in red so: