Question

question
what is the image point of $(-4, -6)$ after the transformation $t_{-3, -1} \circ r_{x\text{-axis}}$?

answer attempt 1 out of 4

Explanation:

Step1: Apply \( r_{x\text{-axis}} \)

The reflection over the \( x \)-axis, \( r_{x\text{-axis}} \), transforms a point \( (x, y) \) to \( (x, -y) \). For \( (-4, -6) \), this gives \( (-4, 6) \).

Step2: Apply \( T_{-3, -1} \)

The translation \( T_{h, k} \) transforms \( (x, y) \) to \( (x + h, y + k) \). Here, \( h = -3 \), \( k = -1 \). Using the result from Step 1, \( (-4 + (-3), 6 + (-1)) = (-7, 5) \).

Answer:

\((-7, 5)\)