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Usimov [2.4K]
3 years 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:
zalisa [80]3 years ago
3 0
We are said that a rectangle has been transformed into the one indicated in Figure 1 according to this rule:

R_0, \ 90^{\circ}

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:

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

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

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. Counterc
lockwise

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

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

By reversing the answer, we have:

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)}

lisov135 [29]3 years ago
3 0

Answer:

Q(4,3)

Step-by-step explanation:

One type of transformation is rotations, which are done counter-clockwise direction.

In this case, we have a rotation of 90° around the origin (0,0), that can be expressed as

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

Which means a 90° rotation would be done by changing coordinates positions and inverting the sign of y-coordinate.

However, the problem is giving the transformed coordinates where Q'(-3,4).

So, applying the rule described above, the original coordinate is Q(4,3).

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