Which of the following rules best describes the matrix below? (picture)

option b

reflection over the line y = x

Step-by-step explanation:

Matrix for every option is mention below

a)

rotation of 90° counter clockwise about the origin

0    -1

1     0

b)

rotation of 180° about the origin

-1    0

0    -1

c)

for a reflection in the line y=x

0    1

1     0

d)

translation 1 unit left and 1 unit up

1      0

0     1

The correct option is b.

Step-by-step explanation:

The rule of rotation of 90° counterclockwise about the origin is defined by the matrix

The rule of reflection of the line y=x is defined by the matrix

The rule of rotation of 180° about the origin is defined by the matrix

The rule of translation of 1 unit left and 1 unit up is defined by the matrix

Only the rule of reflection of the line y=x is defined by the given matrix, therefore the correct option is b.

the answer would be c:   ax + b = ax + c

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm