Question

justify whether the statement is always, sometimes, or never true for translations. the vector \\( \langle a, b \
angle \\) will translate each coordinate of a preimage \\( a \\) units right and \\( b \\) units up. the statement is \\( \square \\) true if \\( a \\) and \\( b \\) are \\( \square \\).

Explanation:

Translation vector \((a,b)\) moves a point \((x,y)\) to \((x + a,y + b)\). If \(a>0\), it moves right; if \(a < 0\), it moves left. If \(b>0\), it moves up; if \(b < 0\), it moves down. So the statement "The vector \((a,b)\) will translate each coordinate of a pre - image \(a\) units right and \(b\) units up" is only true when \(a\geq0\) and \(b\geq0\).

Answer:

The statement is sometimes true if \(a\) and \(b\) are non - negative.