The triangles are congruent by sss or hl. the diagram shows the sequence of three rigid transformations used to map abc onto a"b"c". what is the sequence of the transformations? rotation, then reflection, then translation rotation, then translation, then reflection reflection, then translation, then rotation reflection, then rotation, then translation

The sequence of transformation used to map ABC onto A"B"C" is reflection, then rotation, then translation.

Step-by-step explanation:

To map ABC onto A"B"C" steps are:

step 1: Reflection of ABC

step 2: rotation of A'BC by some angle to obtain A'B'C'.

step 3: translation of A'B'C' by some units to the right to obtain the given transformation A"B"C".

-  The sequence of the transformations for the given diagram must be reflection, then rotation, then translation.

Explanation:-

Given : Four triangles which are congruent by SSS postulate or HL theorem.

According to the given diagram , the rigid transformations are as follows

1. Reflection: ΔABC is flipped about BC to form ΔA'BC such that AC=A'C and its is already given that they are congruent thus the rigid transformation used here is reflection.

2. Rotation:- ΔA'BC is rotated about point A' at some angle to form ΔA'B'C' , and they are congruent (given). Thus the rigid transformation used here is rotation.

3.Translation:- ΔA'B'C' is translated exactly right by some factor to form ΔA"B"C" ∵ all the points have changed but as these triangles are congruent (given) then corresponding parts must be equal.Thus the rigid transformation used here is  translation.

a4 - 3a2 - 1

step-by-step explanation:

step   1   :

equation at the end of step   1   :

  ((a4) -   3a2) -   1

step   2   :

trying to factor by splitting the middle term

2.1     factoring   a4-3a2-1  

the first term is,   a4   its coefficient is   1 .

the middle term is,   -3a2   its coefficient is   -3 .

the last term, "the constant", is   -1  

answer: (1,3) and (-2,0) i think.