Question

The figure shows two triangles on a 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 4, negative 2, vertex B on ordered pair 3, negative 2 and vertex C on ordered pair 3, negative 5. Another triangle A prime B prime C prime is shown with vertex A prime on ordered pair 1, 2, vertex B prime on ordered pair 2, 2 and vertex C prime on ordered pair 2, 5.

What set of transformations is performed on triangle ABC to form triangle A'B'C'?

A 180 degree counterclockwise rotation about the origin followed by a translation 5 units up
A 270 degree counterclockwise rotation about the origin followed by a translation 5 units up
A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin
A translation 5 units to the left followed by a 270 degree counterclockwise rotation about the origin

Answer 1

Vertices of Preimage that is Triangle ABC =A(4,-2), B(3,-2),C(3,-5)

Vertices of image , i.e Δ A'B'C'=A'(1,2),B'(2,2), C'(2,5)

Now, transalation by 5 units left of triangle ABC takes it to

A(4,-2)=(4-5,-2)=(-1,-2)

B(3,-2)=(3-5,-2)=(-2,-2)

C(3,-5)=(3-5,-5)=(-2,-5)

When preimage is rotated through an angle of 180 degree, counterclockwise vertices of triangle (-1,-2),(-2,-2) and (-2,-5) goes to image A'(1,2),B'(2,2), C'(2,5).

Option C: A translation 5 units to the left followed by a 180 degree counterclockwise rotation about the origin takes ΔABC to ΔA'B'C'.