Question

1. reflect the figure through r(-1, -2)

Explanation:

Step1: Identify original points

Original coordinates:
$R(-1, -2)$, $S(-2, -3)$, $T(-4, -2)$, $Y(-3, -3)$

Step2: Reflection formula over point

For a point $(x,y)$ reflected over $(h,k)$, the new point is $(2h-x, 2k-y)$

Step3: Calculate $R'$

$h=-1, k=-2$, $x=-1,y=-2$
$R'=(2(-1)-(-1), 2(-2)-(-2))=(-2+1, -4+2)$

Step4: Calculate $S'$

$x=-2,y=-3$
$S'=(2(-1)-(-2), 2(-2)-(-3))=(-2+2, -4+3)$

Step5: Calculate $T'$

$x=-4,y=-2$
$T'=(2(-1)-(-4), 2(-2)-(-2))=(-2+4, -4+2)$

Step6: Calculate $Y'$

$x=-3,y=-3$
$Y'=(2(-1)-(-3), 2(-2)-(-3))=(-2+3, -4+3)$

Answer:

$R'(-1, -2)$
$S'(0, -1)$
$T'(2, -2)$
$Y'(1, -1)$