Question

#17

Part A

Rectangle PQRS is rotated 90°
counterclockwise about the origin to create rectangle P'Q'R'S' (not shown). What are the coordinates of point R'?
Responses

(−7,6)
( - 7 , 6 )

(7,6)
( 7 , 6 )

(−6,7)
( - 6 , 7 )

(6,7)
( 6 , 7 )
Question 2
Part B

Rectangle PQRS is reflected across the y-axis and then translated down 2 units to create rectangle P''Q''R''S'' (not shown). What are the coordinates of Q''?
Responses

(−6,0)
( - 6 , 0 )

(6,0)
( 6 , 0 )

(−6,−4)
( - 6 , - 4 )

(−6,2)
( - 6 , 2 )

Answer 1

Explanation:

When a rectangle is rotated 90° counterclockwise about the origin, the coordinates change as follows:

Point P (x, y) becomes P' (-y, x)

Point Q (x, y) becomes Q' (-y, x)

Point R (x, y) becomes R' (-y, x)

Point S (x, y) becomes S' (-y, x)

Since we are looking for the coordinates of point R', we substitute the original coordinates of point R into the formula:

R' = (-y, x) = (-(6), 7) = (-6, 7)

Therefore, the coordinates of point R' are (-6, 7).

The correct answer is "(−6,7)" or "( - 6 , 7 )".

Part B:

When a rectangle is reflected across the y-axis, the x-coordinate changes its sign, and the y-coordinate remains the same.

After reflecting across the y-axis, the coordinates become:

Point P'' (x, y) becomes P'' (-x, y)

Point Q'' (x, y) becomes Q'' (-x, y)

Point R'' (x, y) becomes R'' (-x, y)

Point S'' (x, y) becomes S'' (-x, y)

Since we are looking for the coordinates of point Q'', we substitute the original coordinates of point Q into the formula:

Q'' = (-x, y) = (-(6), 0) = (-6, 0)

After reflecting across the y-axis, the rectangle is translated down 2 units. Since the y-coordinate of Q'' is 0, the translation down 2 units does not affect it.

Therefore, the coordinates of point Q'' are (-6, 0).

The correct answer is "(−6,0)" or "( - 6 , 0 )".