Question

riangle 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? (1 point) coordinate plane with triangle ABC at A negative 3 comma 3, B 1 comma negative 3, and C negative 3 comma negative 3

Answer 1

The relationship between segment AC and segment A double prime C double prime is AC = A''C'' /2.

What is a Scale Factor ?

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 = $\rm \sqrt {52}$

A''B'' = $\rm \sqrt{ 8^2 + 12^2}$ = 2 $\rm \sqrt {52}$

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.

To know more about Scale Factor

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