Question

The transformation shown below maps Trapezoid TANS onto Trapezoid TA'N'S! Tell if the pre-image andimage are congruent based on the given information and justify.ation

Answer 1

Given the coordinates of the trapezoid TANS as

$T(-5,-2),A(-5,1),N(-2,3),S(1,2)$

The coordinates of the image T'A'N'S' is

$T^{\prime}(-2,5),A^{\prime}(1,5),N^{\prime}(3,2),S^{\prime}(2,-1)$

From the coordinates of the image given above, it is observed that the transformation rule is

$(x,y)\Rightarrow(y,-x)$

The transformation rule stated above is that of 90 degrees clockwise rotation, and rotation of figures produce congruent figures

Hence, the answer to the question is;

Yes, they are congruent because the image is a rotation of the pre-image and rotation produce congruent figures