Question

which sequence of transformations maps ijkl onto ijkl? a translation left 10 units followed by a rotation 90° counterclockwise around the origin a translation down 8 units followed by a reflection across the y - axis a rotation 90° counterclockwise around the origin followed by a reflection across the x - axis

Explanation:

Step1: Analyze translation - left 10 units

If we first translate left 10 units, the x - coordinates of points in IJKL will decrease by 10. Then rotating 90° counter - clockwise around the origin uses the transformation rule \((x,y)\to(-y,x)\). This sequence will not map IJKL onto I'J'K'L'.

Step2: Analyze translation - down 8 units

If we first translate down 8 units, the y - coordinates of points in IJKL will decrease by 8. Then reflecting across the y - axis uses the transformation rule \((x,y)\to(-x,y)\). Let's assume a point \((x,y)\) in IJKL. After translation down 8 units, it becomes \((x,y - 8)\), and after reflection across the y - axis, it becomes \((-x,y - 8)\). This sequence maps IJKL onto I'J'K'L'.

Step3: Analyze rotation - 90° counter - clockwise first

If we first rotate 90° counter - clockwise around the origin, \((x,y)\to(-y,x)\). Then reflecting across the x - axis uses the transformation rule \((x,y)\to(x,-y)\). This sequence will not map IJKL onto I'J'K'L'.

Answer:

a translation down 8 units followed by a reflection across the y - axis