Question

figure f is the result of a transformation on figure e. which transformation would accomplish this? answer a reflection over the x -axis a translation 2 units to the right and 6 units down a reflection over the y -axis a rotation 180° clockwise about the origin

Explanation:

Step1: Analyze reflection over x - axis

When a figure is reflected over the x - axis, the rule is (x,y)→(x, - y). The orientation of the figure would change in a way that is not consistent with Figure E to Figure F.

Step2: Analyze reflection over y - axis

When a figure is reflected over the y - axis, the rule is (x,y)→( - x,y). This does not match the transformation from Figure E to Figure F.

Step3: Analyze translation

For a translation 2 units to the right and 6 units down, the rule is (x,y)→(x + 2,y - 6). If we take a point on Figure E, say the top - left vertex at (-4,4), applying the translation: (-4,4)→(-4 + 2,4 - 6)=( - 2,-2). This is not correct for the transformation.

Step4: Analyze rotation 180° clockwise about the origin

The rule for a 180° clockwise rotation about the origin is (x,y)→(-x,-y). For a point on Figure E like (-4,4), (-4,4)→(4,-4); for the point (-4,0), (-4,0)→(4,0); for the point (-2,3), (-2,3)→(2,-3). This matches the transformation from Figure E to Figure F.

Answer:

A rotation 180° clockwise about the origin