Question

on the set of axes below, △let and △let are graphed in the coordinate plane where △let≅△let. which sequence of rigid motions maps △let onto △let? (1) a reflection over the y - axis followed by a reflection over the x - axis (2) a rotation of 180° about the origin (3) a rotation of 90° counterclockwise about the origin followed by a reflection over the y - axis (4) a reflection over the x - axis followed by a rotation of 90° clockwise about the origin

Explanation:

Step1: Recall transformation rules

A rotation of 180° about the origin changes the sign of both the x - and y - coordinates of each point. Let the coordinates of a point in \(\triangle LET\) be \((x,y)\). After a 180° rotation about the origin, the new coordinates \((x',y')=(-x,-y)\).

Step2: Analyze other options

A reflection over the y - axis changes the sign of the x - coordinate (\((x,y)\to(-x,y)\)) and then a reflection over the x - axis changes the sign of the y - coordinate (\((-x,y)\to(-x, - y)\), but the orientation of the figure is not correct as per the given triangles. A 90° counter - clockwise rotation about the origin changes \((x,y)\to(-y,x)\) and then a y - axis reflection changes \((-y,x)\to(y,x)\) which is incorrect. A reflection over the x - axis changes \((x,y)\to(x,-y)\) and then a 90° clockwise rotation about the origin changes \((x,-y)\to(-y,-x)\) which is also incorrect.

Answer:

(2) a rotation of 180° about the origin