Question

Two similar triangles are shown on the coordinate grid: A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A triangle ABC is shown with vertex A on ordered pair negative 2, negative 1, vertex B on ordered pair 0, 0, and vertex C on ordered pair 1, negative 3. A triangle A prime B prime C prime is also shown with vertex A prime on ordered pair negative 4, 2 , vertex B prime on ordered pair 0, 0 and vertex C prime on ordered pair 2, 6. Which set of transformations has been performed on triangle ABC to form triangle A'B'C'? Dilation by a scale factor of 4 followed by reflection about the x-axis Dilation by a scale factor of 2 followed by reflection about the x-axis Dilation by a scale factor of 4 followed by reflection about the y-axis Dilation by a scale factor of 2 followed by reflection about the y-axis\

Answer 1

The set of transformation that has been performed on triangle ABC

to form triangle A'B'C' is " Dilation by a scale factor of 2 followed by

reflection about the x-axis " ⇒ 2nd answer

Explanation:

Lets revise some important rules

The corresponding sides of similar triangles have constant ratio

Dilation makes a triangle and its image similar

Reflection about x-axis change the sign of the y-coordinate of a point after reflected about the x-axis

Δ ABC and Δ A'B'C are similar after set of transformations has been

performed on Δ ABC to form Δ A'B'C'

∵ The vertices of triangle ABC are:

A = (-2 , -1) , B = (0 , 0) , C = (1 , -3)

∵ The vertices of triangle A'B'C' are:

A' = (-4 , 2) , B' = (0 , 0) , C' = (2 , 6)

∵ x-coordinate of point A = -2 and x-coordinate of point A' = -4

∵ y-coordinate of point A = -1 and y-coordinate of point A' = 2

∵ x-coordinate of point B = 0 and x-coordinate of point B' = 0

∵ y-coordinate of point B = 0 and y-coordinate of point B' = 0

∵ x-coordinate of point C = 1 and x-coordinate of point C' = 2

∵ y-coordinate of point C = -3 and y-coordinate of point C' = 6

∵ Each coordinate of the vertices A , B , C is multiplied by 2 to give

the coordinates of the of the vertices A' , B' , C'

∴ Δ ABC is dilated by scale factor of 2

∵ The signs of y-coordinates of the vertices A , B , C is opposite to

the signs of y-coordinates of the of the vertices A' , B' , C'

∴ Δ ABC is reflected about the x-axis

The set of transformation that has been performed on triangle ABC

to form triangle A'B'C' is " Dilation by a scale factor of 2 followed by

reflection about the x-axis "