Question

name____ cohort____ grade 8: week of 9/15, math hw - due septem directions: show all steps of your thinking and c problem #1 - unit 1 (mild) which describes a sequence of rigid motions that maps abcde onto a\b\c\d\e\? 1) a rotation of 90° counterclockwise about the origin followed by a reflection over the x - axis 2) a rotation of 90° counterclockwise about the origin followed by a translation down 7 units 3) a reflection over the y - axis followed by a reflection over the x - axis 4) a reflection over the x - axis followed by a rotation of 90° counterclockwise about the origin

Explanation:

Step1: Recall rigid - motion transformations

Rigid motions include rotations, reflections, and translations. Analyze each option.

Step2: Analyze option 1

A 90 - degree counter - clockwise rotation about the origin and then a reflection over the x - axis will not map the figure as required.

Step3: Analyze option 2

A 90 - degree counter - clockwise rotation about the origin followed by a translation down 7 units will map the figure. Let's assume a general point \((x,y)\) in \(ABCDE\). A 90 - degree counter - clockwise rotation about the origin transforms \((x,y)\) to \((-y,x)\). Then a translation down 7 units transforms \((-y,x)\) to \((-y,x - 7)\) which can map the points of \(ABCDE\) to \(A''B''C''D''E''\).

Step4: Analyze option 3

A reflection over the y - axis followed by a reflection over the x - axis will not map the figure as required.

Step5: Analyze option 4

A reflection over the x - axis followed by a 90 - degree counter - clockwise rotation about the origin will not map the figure as required.

Answer:

1. a rotation of 90° counterclockwise about the origin followed by a translation down 7 units