Question

what is the image point of (0, 7) after the transformation $t_{3,0} \circ r_{y=-x}$?
answer attempt 1 out of 2

Explanation:

Step1: Apply reflection \( r_{y = -x} \)

The reflection over the line \( y=-x \) has the rule \( (x,y)\to(-y,-x) \). For the point \( (0,7) \), substitute \( x = 0 \) and \( y = 7 \) into the rule:
\( (0,7)\to(-7,-0)=(-7,0) \).

Step2: Apply translation \( T_{3,0} \)

The translation \( T_{3,0} \) (which means translating 3 units right and 0 units up) has the rule \( (x,y)\to(x + 3,y+0) \). For the point \( (-7,0) \), substitute \( x=-7 \) and \( y = 0 \):
\( (-7,0)\to(-7 + 3,0)=( - 4,0) \).

Answer:

\((-4, 0)\)