Question

question what is the image point of (-6, -8) after the transformation $r_{y = -x}circ t_{3,-2}$? answer attempt 1 out of 2

Explanation:

Step1: First perform the translation

The translation $T_{3,-2}$ means adding 3 to the $x$-coordinate and subtracting 2 from the $y$-coordinate.
For the point $(-6,-8)$, after translation:
$x_1=-6 + 3=-3$
$y_1=-8-2=-10$
The new - point after translation is $(-3,-10)$.

Step2: Then perform the reflection

The reflection $r_{y = -x}$ has the transformation rule $(x,y)\to(-y,-x)$.
For the point $(-3,-10)$, after reflection:
$x_2=-(-10) = 10$
$y_2=-(-3)=3$

Answer:

$(10,3)$