riangle ABC is transformed to obtain triangle A′B′C′:

A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.? (5 points)

Group of answer choices

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees

Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees

Triangle ABC is similar to triangle A prime B prime C prime. because triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees

Option b: Triangle A prime B prime C prime. is obtained by dilating Triangle ABC by a scale factor of 1 over 3 and then rotating it about the origin by 180 degrees.

What happens when a triangle is dilated?

If a triangle is dilated by scale factor, the base and height are known to be altered by the scale factor and also the area is also altered by the said factor.

Note that if there is a scale distances between points, dilations do not alter angles.

Since:

A'(-1, -1) = (-1/2) × A(2, 2)

B'(-1, -5) = (-1/2) × B(2, 10)

C'(-4, -6) = (-1/2) × C(8, 12)

Rotation by 180° negates is seen in both of the coordinates. It is said to be the equivalent to reflection across the x-axis and also the reflection across the y-axis.

Therefore, The statement that correct for Triangle ABC. and Triangle A prime B prime C prime is:

Option b: Triangle A prime B prime C prime. is obtained by dilating Triangle ABC by a scale factor of 1 over 3 and then rotating it about the origin by 180 degrees.

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