Question

If rectangle STUV is translated using the rule (x, y) → (x - 2, y - 4) and then rotated 90° counterclockwise, what is the location of S''? (3, -9) (3, -4) (-2, -4) (-2, -9)

Answer 1

The correct option is d.

The location of S″ is (-7, -1).

To find the location of point S″ after translating and rotating the rectangle STUV, we'll follow these steps step by step:

1. Translate the rectangle using the rule (x, y) → (x - 2, y - 4):

• S'(x, y) = S(x - 2, y - 4)

2. Rotate the translated point S' 90° counterclockwise:

To rotate a point (x, y) counterclockwise by 90°, swap its x and y coordinates and negate the new x-coordinate:

• S″(x, y) = S'(y, -x)

Now, let's apply these transformations to point S:

1. Translate point S by (x - 2, y - 4):

• S'(x, y) = S(x - 2, y - 4)

2. Rotate point S' counterclockwise:

• S″(x, y) = S'(y, -x)

Now, we'll substitute the coordinates of point S (S(x, y)) into these equations:

• S(x, y) = S(x - 2, y - 4)
• S′(x, y) = S(y - 4, x - 2)

Now, we can find S″(x, y):

• S″(x, y) = S′(y - 4, x - 2)
• S″(x, y) = (y - 4, x - 2)

So, the location of S″ is (y - 4, x - 2).

Now, let's find the coordinates of S″:

• For point S, we have S(x, y) = S(1, -3) because you haven't provided the coordinates of point S.
• Substituting these values into the equation for S″:
• S″(x, y) = (y - 4, x - 2)
• S″(1, -3) = (-3 - 4, 1 - 2)
• S″(1, -3) = (-7, -1)

So, The answer is (-7, -1).

The complete question is here:

If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of S″?

A. (3, −9)

B. (3, −4)

C. (−2, −4)

D. (-7, -1)

Answer 2

The location of S" after translating and rotating the rectangle is d. (-2, -9)

How to determine the location of S''

From the question, we have the following parameters that can be used in our computation:

S = (-7, 6)

Also, we have the following rule

Translation by the rule (x, y) → (x − 2, y − 4)

This means that we subtract 2 from the x coordinate and 4 from the y coordinates

So, we have

S' = (-7 - 2, 6 - 4)

S' = (-9, 2)

Next, we rotate the translated rectangle 90° counterclockwise.

Here, we have

(x, y) = (-y, x)

So, we have

S'' = (-2, -9)

Hence, the location of S" is (-2, -9).

Question

If rectangle STUV is translated using the rule (x, y) → (x - 2, y - 4) and then rotated 90° counterclockwise, what is the location of S''?

(3, -9)

(3, -4)

(-2, -4)

(-2, -9)

See attachment