Question

The figure shows two triangles on a coordinate grid: A coordinate plane with two triangles is shown. Triangle RST has vertices R at 3 comma 4, S at 1 comma 1, and T at 5 comma 1. Triangle R prime S prime T prime has vertices R prime at 2 comma negative 3, S prime at negative 1 comma negative 1 and T prime at negative 1 comma negative 5. What set of transformations is performed on triangle RST to form triangle R’S’T’? A 90-degree counterclockwise rotation about the origin followed by a translation 2 units left A 270-degree counterclockwise rotation about the origin followed by a translation 2 units to the right A translation 2 units down followed by a 90-degree counterclockwise rotation about the origin A translation 2 units down followed by a 270-degree counterclockwise rotation about the origin Question 4(Multiple Choice Worth 4 points) (02.03)Figure EFGH is transformed to E’F’G’H’, as shown: A coordinate plane is shown. Figure EFGH has vertices E at negative 5 comma 4, F at negative 5 comma 1, G at negative 3 comma 2, and H at negative 1 comma 6. Figure E prime F prime G prime H prime has vertices at E prime 7 comma 4, F prime 7 comma 1, G prime 5 comma 2 and H prime 3 comma 6. Which of the following sequences of transformations is used to obtain figure E’F’G’H’ from EFGH? Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units Reflection about the y-axis followed by a translation right by 2 units Reflection about the x-axis followed by a translation left by 2 units Question 5(Multiple Choice Worth 4 points) (02.03)Which statement is true about the result of a rigid transformation? The image will be larger than the pre-image. The pre-image will be larger than the image. Each one is unique; no general statement can be made about size.

Answer 1

Answer:

C,  "A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left" should be the right answer.

Step-by-step explanation:

Solution:

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'.