The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
The ratio by which the new image is bigger or smaller than the original image is the scale factor.
It is given that
Triangle A″B″C″ is formed using the translation (x + 0, y + 2)
and the dilation by a scale factor of 2 from the origin.
coordinate plane with triangle ABC at A (- 3, 3), B (1, - 3), and C (- 3, -3).
segment AC is equal to A''C'' over 2
Scale factor = 2
The coordinates are
A (- 3, 3), B (1, - 3), and c (- 3, -3) is translated using (x + 2, y + 0),
new coordinates
A'(- 1, 3), B'(3, - 3), and C'(- 1, -3).
The dilation by a scale factor of from the origin
A″ (-2, 6), B″ (6, -6) and C″(-2, -6)
By the distance formula
AB = [tex]\rm \sqrt {52}[/tex]
A''B'' = [tex]\rm \sqrt{ 8^2 + 12^2}\\[/tex] = 2 [tex]\rm \sqrt {52}[/tex]
Therefore
AB = A''B'' /2
Similarly AC = A''C'' /2
The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.
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