Question

determine a series of transformations that would map figure i onto figure j.

Explanation:

Step1: Reflect over the x - axis

When a point \((x,y)\) is reflected over the \(x\) - axis, the transformation rule is \((x,y)\to(x, - y)\). This will flip Figure \(I\) vertically.

Step2: Translate 6 units up

The translation rule for moving a point \((x,y)\) up by \(k\) units is \((x,y)\to(x,y + k)\). Here \(k = 6\), so \((x,y)\to(x,y+6)\).

Step3: Translate 7 units left

The translation rule for moving a point \((x,y)\) left by \(h\) units is \((x,y)\to(x - h,y)\). Here \(h=7\), so \((x,y)\to(x - 7,y)\)

Answer:

A reflection over the \(x\) - axis, a translation \(6\) units up and \(7\) units left.