Question

type the coordinates of the images s, r, and t for each of the following points under the translation defined by (x,y) → (x + 3, y - 8)
a) s(7,14) b) r(- 8, - 3) c) t(a,b)
a) s(7,14)→s (10,6) (type an ordered pair )
b) r(- 8, - 3)→r (-5,-11) (type an ordered pair )
c) t(a,b)→t \square (type an ordered pair )

Explanation:

Step1: Apply the translation rule to point \(R\)

For a point \((x,y)\) under the translation \((x,y)\to(x + 3,y-8)\), when \(x=-8\) and \(y = - 3\), the \(x\) - coordinate of the image is \(x+3=-8 + 3=-5\), and the \(y\) - coordinate of the image is \(y - 8=-3-8=-11\). So \(R(-8,-3)\to R'(-5,-11)\)

Step2: Apply the translation rule to point \(T\)

When \(x = a\) and \(y = b\), the \(x\) - coordinate of the image \(T'\) is \(x+3=a + 3\), and the \(y\) - coordinate of the image \(T'\) is \(y-8=b-8\). So \(T(a,b)\to T'(a + 3,b-8)\)

Answer:

b) \((-5,-11)\)
c) \((a + 3,b-8)\)