Question

answer attempt 1 out of 2
a rotation 90° clockwise about the
origin
a translation 2 units to the left and 8
units up
a translation 2 units to the right and
8 units down
a rotation 90° counterclockwise
about the origin
submit ans

Explanation:

Step1: Analyze translation

Translation involves moving a figure without rotation. Looking at the vertical distance between corresponding points of Figure L and Figure K: \(5 - (- 3)=8\) (downward). Horizontal distance: \(5 - 3 = 2\) (right - ward). A translation 2 units to the right and 8 units down can map Figure L to Figure K.

Step2: Analyze rotation

For a \(90^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\), for a \(90^{\circ}\) counter - clockwise rotation about the origin \((x,y)\to(-y,x)\). If we take a point from Figure L, say \((1,3)\). After \(90^{\circ}\) clockwise rotation \((3,-1)\) (not a point on Figure K). After \(90^{\circ}\) counter - clockwise rotation \((- 3,1)\) (not a point on Figure K).

Answer:

A translation 2 units to the right and 8 units down