In geometry, translation is the movement of a point or shape from one position to another.
The translation from [tex]\triangle ABC[/tex] to [tex]\triangle A'B'C'[/tex] is [tex](x,y) \to (x + 1, x - 3)[/tex]
Given that:
[tex]A = (5,1) \to A' = (6,-2)[/tex]
[tex]B = (-2,3) \to B' = (-1,0)[/tex]
The transformation is calculated as follows:
[tex](x,y) = (x + a, x + b)[/tex]
Using A and A', we have:
[tex](6,-2) = (5 + a, 1 + b)[/tex]
By comparison:
[tex]5 + a = 6[/tex] and [tex]-2 = 1 + b[/tex]
So, we have:
[tex]5 + a = 6[/tex]
[tex]a = 6 - 5[/tex]
[tex]a = 1[/tex]
[tex]-2 = 1 + b[/tex]
[tex]b =-2 - 1[/tex]
[tex]b = -3[/tex]
Recall that:
[tex](x,y) = (x + a, x + b)[/tex]
So, we have:
[tex](x,y) = (x + 1, x - 3)[/tex]
Hence, the translation of the triangle is:
[tex](x,y) \to (x + 1, x - 3)[/tex]
Read more about translations at:
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