Question

Trapezoid ABCD shown below will undergo a single transformation.

(6,4) (3,4) (0,0) (9,0)
Which type of transformation could result in a trapezoid for which the image of every point in ABCD is itself?
translation
rotation about the origin
reflection
dilation (scale factor not 1)
none of the above

Answer 1

The transformation that could be applied to ABCD is:

• Translation .

• Rotation about the origin.

Explanation:

Trapezoid ABCD is given with coordinates A(6,4) , B(3,4) , C(0,0) , D(9,0)

Now we are asked to find which transformation will map every point in ABCD to itself.

This means that the figure after transformation will come to it's original place.

Hence such a transformation will be:

1)

Translation.

Since on translating a figure by the rule:

(x,y) → (x+0,y+0)

2)

Rotation about the origin.

When we rotate a figure 360 degree or by some integer multiple of 360 degree about the origin then the figure attains the original position.

Answer 2

Translation by (0, 0) or rotation by any integer multiple of 360° will map the figure to itself.