MATH SOLVE

6 months ago

Q:
# A rectangle is transformed according to the rule r0, 90º. 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?

Accepted Solution

A:

We are said that a rectangle has been transformed into the one indicated in Figure 1 according to this rule:

[tex]R_0, \ 90^{\circ}[/tex]

We know that the center of rotation is origin and two rules are applied to rotate a point 90 degrees, namely:

1. Clockwise

In this case, the rule to transform a point is:

[tex](x,y) \rightarrow (y,-x)[/tex]

This rule was already applied to form the image, so all we need to do is to reverse the answer using this formula, therefore:

[tex]For \ Q(-3,4): \\ \\ (y,-x)=(-3,4) \\ \\ \therefore y=-3 \ and \ -x=4 \therefore x=-4 \\ \\ Thus, \ the \ point \ is: \\ \\ \boxed{Q(-4,-3)}[/tex]

2. Counterclockwise

Applying the same previous concept but with the new rules for this case:

[tex](x,y) \rightarrow (-y,x)[/tex]

By reversing the answer, we have:

[tex]For \ Q(-3,4): \\ \\ (-y,x)=(-3,4) \\ \\ \therefore -y=-3 \therefore y=3 \ and \ x=4 \\ \\ Thus, \ the \ point \ is: \\ \\ \boxed{Q(4,3)}[/tex]

[tex]R_0, \ 90^{\circ}[/tex]

We know that the center of rotation is origin and two rules are applied to rotate a point 90 degrees, namely:

1. Clockwise

In this case, the rule to transform a point is:

[tex](x,y) \rightarrow (y,-x)[/tex]

This rule was already applied to form the image, so all we need to do is to reverse the answer using this formula, therefore:

[tex]For \ Q(-3,4): \\ \\ (y,-x)=(-3,4) \\ \\ \therefore y=-3 \ and \ -x=4 \therefore x=-4 \\ \\ Thus, \ the \ point \ is: \\ \\ \boxed{Q(-4,-3)}[/tex]

2. Counterclockwise

Applying the same previous concept but with the new rules for this case:

[tex](x,y) \rightarrow (-y,x)[/tex]

By reversing the answer, we have:

[tex]For \ Q(-3,4): \\ \\ (-y,x)=(-3,4) \\ \\ \therefore -y=-3 \therefore y=3 \ and \ x=4 \\ \\ Thus, \ the \ point \ is: \\ \\ \boxed{Q(4,3)}[/tex]