Question

construct the following transformation on qt: y=3 q(0,7) t(4,3) q( , ) t(4,3) multiple-choice question so where is t? the same location as t. different location from t.

Explanation:

Step1: Analyze the reflection over \( y = 3 \) for point \( T(4,3) \)

The formula for reflecting a point \( (x,y) \) over the horizontal line \( y = k \) is \( (x, 2k - y) \). Here, \( k = 3 \) and the point \( T \) is \( (4,3) \).

Step2: Apply the reflection formula

Substitute \( x = 4 \), \( y = 3 \), and \( k = 3 \) into the formula: \( 2k - y = 2\times3 - 3 = 6 - 3 = 3 \). The \( x \)-coordinate remains \( 4 \), and the new \( y \)-coordinate is \( 3 \). So the reflected point \( T' \) has the same coordinates as \( T \).

Answer:

The coordinates of \( T' \) are \( (4,3) \) (the same as \( T \) because the distance from \( T \) to \( y = 3 \) is \( 0 \), so reflecting it over \( y = 3 \) leaves it unchanged).