Question

1. describe the translation that moves every point of a preimage 4 units left and 6 units up by using coordinates.

Explanation:

Step1: Recall translation rules

In coordinate geometry, for a point \((x,y)\), moving left or right affects the \(x\)-coordinate (left is subtraction, right is addition) and moving up or down affects the \(y\)-coordinate (up is addition, down is subtraction).

Step2: Apply left and up movement

Moving 4 units left: the \(x\)-coordinate changes by \(- 4\) (since left is negative direction on \(x\)-axis). Moving 6 units up: the \(y\)-coordinate changes by \(+6\) (since up is positive direction on \(y\)-axis). So if a pre - image point is \((x,y)\), the image point after translation will be \((x - 4,y+6)\). The translation vector (or the rule for translation) can be represented as \((x,y)\to(x - 4,y + 6)\) or in terms of the translation \((h,k)\) where \(h=-4\) and \(k = 6\) (the translation \((h,k)\) means moving \(h\) units horizontally and \(k\) units vertically, with \(h<0\) for left, \(h > 0\) for right, \(k>0\) for up and \(k < 0\) for down).

Answer:

For a point \((x,y)\) in the pre - image, the translation is given by \((x,y)\to(x - 4,y + 6)\) (or the translation vector is \(\langle- 4,6
angle\), meaning 4 units left and 6 units up).