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

Question

Aleksandr

10 days ago

7

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?

Mathematics

2 answers:

babunello [11.8K] · Answer 1 · 2026-04-06T00:19:16+03:00

We understand that a rectangle has been altered into the one shown in Figure 1 using this rule:

$R_0, \ 90^{\circ}$

It is known that the origin is the center of rotation and two rules apply to perform a rotation of 90 degrees, namely:

1. Clockwise

The rule to convert a point in this case is:

$(x,y) \rightarrow (y,-x)$

This rule has already been implemented to create the image, so we need to reverse the outcome using this formula, hence:

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

2. Counterclockwise

Applying the same concept as before but with new rules for the scenario:

$(x,y) \rightarrow (-y,x)$

Reversing the outcome gives us:

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

zzz [12.3K] · Answer 2 · 2026-04-06T00:22:41+03:00

Answer:

$Q(4,3)$

Step-by-step explanation:

Rotations are a type of transformation, typically carried out in a counter-clockwise direction.

In this instance, there is a 90° rotation at the origin (0,0), which can be defined as

$(x,y) \implies (-y,x)$

This signifies that during a 90° rotation, the positions of the coordinates are altered while the sign of the y-coordinate is reversed.

However, the problem presents the altered coordinates where $Q'(-3,4)$ .

Thus, by applying the aforementioned rule, we obtain the original coordinate $Q(4,3)$ .