Question

plz help
Rectangle ABCD is congruent to rectangle.

Which sequence of transformations could have been used to transform rectangle ABCD to produce rectangle ?



A.
Rectangle ABCD was rotated 90° clockwise around the origin and then translated 7 units left.

B.
Rectangle ABCD was rotated 90°counterclockwise around the origin and then reflected across the x-axis.

C.
Rectangle ABCD was rotated 90° counterclockwise around the origin and then translated 8 units down.

D.
Rectangle ABCD was rotated 90° clockwise around the origin and then reflected across the y-axis

Answer 1

@welshfella

Answer 2

Any one please help

Answer 3

@justuu

Answer 4

i did

Answer 5

@sammixboo
@dan815
@Compassionate

Answer 6

there is a formula we can use to rotate about an angle

Answer 7

$$
R(90^\circ) = \begin{bmatrix}
0 & -1 \\[3pt]
1 & 0 \\
\end{bmatrix}
$$

Answer 8

$$
\Large{
\begin{bmatrix}
x' \\
y' \\
\end{bmatrix} = \begin{bmatrix}
\cos \theta & -\sin \theta \\
\sin \theta & \cos \theta \\
\end{bmatrix}\begin{bmatrix}
x \\
y \\
\end{bmatrix}
}
$$

Answer 9

so the rotation of 90 degrees counter-clockwise causes
$$ \Large (x,y) \to (-y, x ) $$

Answer 10

so lets look at the transformation of point B(3,1), which I picked arbitrarily
first it rotates counterclockwise, then it translates down 8 units
$$
\Large{
(3,1) \to (-1,3) \to (-1,3-8)= (-1, -5)
}
$$