Question

a translation moves point v (-2, 3) to v (-2, 7). which are true statements about the translation? choose two correct answers. the transformation rule is (x, y) → (x + 0, y + 4). the image is four units to the left of the pre - image. the transformation is a vertical translation. the translation can be described as (x, y) → (x - 2, y + 7). the point moves two units left and four units up.

Explanation:

Step1: Analyze the translation of the x - coordinate

The x - coordinate of point \(V(-2,3)\) to \(V'(-2,7)\) has no change (\(-2=-2\)). In the translation rule \((x,y)\to(x + a,y + b)\), \(a = 0\).

Step2: Analyze the translation of the y - coordinate

The y - coordinate changes from \(y = 3\) to \(y=7\). Using the formula \(y + b\), we have \(3 + b=7\), so \(b = 4\). The translation rule is \((x,y)\to(x+0,y + 4)\).

Step3: Determine the nature of the translation

Since the x - coordinate does not change and only the y - coordinate changes, it is a vertical translation.

Answer:

The transformation rule is \((x,y)\to(x + 0,y+4)\); The transformation is a vertical translation.