Question

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. Which equation explains the relationship between segment AC and segment A double prime C double prime? coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3 segment AC over segment A double prime C double prime = 2 segment A double prime C double prime over segment AC = one half segment AC = segment A double prime C double prime over 2

Answer 1

After performing a translation and a dilation by a scale factor of 2 from the origin, segment A"C" is twice as long as segment AC.

Step-by-step explanation:

The relationship between segment AC and segment A"C" after performing a translation and a dilation by a scale factor of 2 from the origin is that segment A"C" will be twice as long as segment AC. This transformation scales all lengths in the triangle by a factor of 2, and since the translation moves every point in the triangle by the same amount, it does not affect the relative lengths of the segments within the triangle.

The correct equation that explains the relationship between segment AC and segment A"C" is:

segment AC over segment A"C" = 1/2

Meaning that the length of segment AC is half the length of segment A"C" after the transformation.

Answer 2

segment AC is equal to A''B'' over 2

Step-by-step explanation:

Given that,

Scale factor = 2

The coordinates of A is (-3,3)

The coordinates of B is (1,-3)

The coordinates of C is (-3,3)

We know that, the ratio of length of new segment to the length of segment of original figure is called scale factor.

So.

`(A''B'')/(AC)=2\\\\\text{On cross multiplying,}\\\\AC=(A''B'')/(2)`

It means, segment AC is equal to A''B'' over 2 is the correct answer.