a rectangle is transformed according to the rule ( r_{0,90^{circ}} ). the image of the rectangle has…

a rectangle is transformed according to the rule ( r_{0,90^{circ}} ). the image of the rectangle has vertices located at ( r(-4,4) ), ( s(-4,1) ), ( p(-3,1) ), and ( q(-3,4) ). what is the location of ( q )?\n( (-4,-3) )\n( (-3,-4) )\n( (3,4) )\n( (4,3) )

a rectangle is transformed according to the rule ( r_{0,90^{circ}} ). the image of the rectangle has vertices located at ( r(-4,4) ), ( s(-4,1) ), ( p(-3,1) ), and ( q(-3,4) ). what is the location of ( q )?\n( (-4,-3) )\n( (-3,-4) )\n( (3,4) )\n( (4,3) )

Answer

Explanation:

Step1: Recall the rotation rule

The rule for a (90^{\circ}) counter - clockwise rotation about the origin (R_{0,90^{\circ}}) is ((x,y)\to(-y,x)). To find the pre - image, we use the inverse rule ((x,y)\to(y, - x)) for a (90^{\circ}) clockwise rotation (since rotation (R_{0,90^{\circ}}) and its inverse are related).

Step2: Apply the inverse rotation rule to (Q'(-3,4))

Let ((x',y')=(-3,4)). Using the formula ((x,y)=(y',-x')). Substitute (x'=-3) and (y' = 4) into the formula: (x = 4) and (y=-(-3)=3)

Answer:

((4,3))