The figure shows two triangles on a coordinate grid:

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 down

a translation 5 units down followed by a 180-degree counterclockwise rotation about the origin

a 270-degree counterclockwise rotation about the origin followed by a translation 5 units to the right

a translation 5 units to the right followed by a 270-degree counterclockwise rotation about the origin

A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin .

Step-by-step explanation:

From the given figure, the coordinates of ΔABC are A(-3,4), B(-3,1), C(-2,1) and the coordinates of ΔA'B'C' are A'(3,1), B'(3,4), C'(2,4).

When, a translation of 5 units down is applied to  ΔABC, the coordinates of the image will be

Then applying 180° counterclockwise rotation about the origin, the coordinates of the image will be :-

which are the coordinates of ΔA'B'C'.

Hence, the set of transformations is performed on triangle ABC to form triangle A’B’C’ is " A translation 5 units down followed by a 180-degree counterclockwise rotation about the origin ".

option (b) is correct

step-by-step explanation:

to find the solution of this system, we need to convert it into reduced row-echelon form. we have,

after applying row operations r2 -> r2/2 and r3 -> r3/3, we get,

a28=58

step-by-step explanation:

a1=a1+(n-1)d

a28= 4+ (28-1)2

a28=4+(27)(2)

a28=4+54

a28=58