What series of transformations would carry the trapezoid onto itself? these are the answers
(x + 0, y − 4), 90° clockwise rotation, reflection over the y-axis
(x + 0, y − 4), 180° rotation, reflection over the y-axis
(x + 6, y + 0), 90° clockwise rotation, reflection over the x‐axis
(x + 6, y + 0), 180° rotation, reflection over the x‐axis

9514 1404 393

  (x + 6, y + 0), 180° rotation, reflection over the x‐axis

Step-by-step explanation:

A rotation 90° and a reflection over an axis will result in a figure 90° rotated from the one shown. That rotation cannot be part of the answer.

If reflection is to be over the y-axis after a rotation of 180°, the translation must amount to a reflection over the x-axis. That is not possible with this shape.

However, translating to the right, in to the first quadrant can be effectively a reflection over the y-axis. Then 180° rotation and reflection over the x-axis will map the figure to itself. This set of transformations is described in the last answer choice:

  (x + 6, y + 0), 180° rotation, reflection over the x‐axis

13

step-by-step explanation:

169-1=168

168-3=165

165-5=160

160-7=153

153-9=144

144-11=133

133-13=120

120-15=105

105-17=88

88-19=69

69-21=48

48-23=25

25-25=0

since it took 13times to completely subtract it hence its square root is 13