Question

which of the following transformations maps abcde onto abcde? translation right 13 units and up 11 units translation right 12 units and up 11 units reflection across the x - axis reflection across the y - axis rotation 90° clockwise around the origin rotation 90° counterclockwise around the origin rotation 180° around the origin

Explanation:

Step1: Analyze translation

Translation involves moving a figure without rotation or reflection. Count the horizontal and vertical displacements of a point. For example, if we take point A and its corresponding point A'. The x - coordinate of A is around - 9 and of A' is around 4, so the horizontal displacement is \(4-(-9)=13\) units to the right. The y - coordinate of A is around - 7 and of A' is around 4, so the vertical displacement is \(4 - (-7)=11\) units up.

Step2: Analyze reflection

For reflection across the x - axis, the y - coordinates of the points of the original figure change their signs. For reflection across the y - axis, the x - coordinates of the points of the original figure change their signs. The orientation of the figure in the given problem does not match the result of x - axis or y - axis reflection.

Step3: Analyze rotation

For a 90° clock - wise rotation around the origin, the transformation rule for a point \((x,y)\) is \((y,-x)\). For a 90° counter - clockwise rotation around the origin, the transformation rule for a point \((x,y)\) is \((-y,x)\). For a 180° rotation around the origin, the transformation rule for a point \((x,y)\) is \((-x,-y)\). The orientation of the figure does not match the result of these rotations.

Answer:

translation right 13 units and up 11 units