Question

1. the coordinates of wxyz are w(-6, -1), x(-5, -3), y(-2, 3), and z(-3, 1). after a translation 8 units right and 3 units down, the coordinates of the image are w (__, ), x (, ), y (, ), and z (, __) 2. which of the number figures are translations of the shaded figure?

Explanation:

Step1: Apply translation rule for x - coordinate

For a translation \(h\) units right, the rule for the \(x\) - coordinate of a point \((x,y)\) is \(x'=x + h\). Here \(h = 2\).
For point \(W(-6,-1)\): \(x=-6\), \(x'=-6 + 2=-4\)
For point \(X(-5,-3)\): \(x=-5\), \(x'=-5 + 2=-3\)
For point \(Y(-2,3)\): \(x=-2\), \(x'=-2+2 = 0\)
For point \(Z(-3,1)\): \(x=-3\), \(x'=-3 + 2=-1\)

Step2: Apply translation rule for y - coordinate

For a translation \(k\) units down, the rule for the \(y\) - coordinate of a point \((x,y)\) is \(y'=y - k\). Here \(k = 3\).
For point \(W(-6,-1)\): \(y=-1\), \(y'=-1-3=-4\)
For point \(X(-5,-3)\): \(y=-3\), \(y'=-3 - 3=-6\)
For point \(Y(-2,3)\): \(y = 3\), \(y'=3-3 = 0\)
For point \(Z(-3,1)\): \(y = 1\), \(y'=1-3=-2\)

Answer:

\(W'(-4,-4)\), \(X'(-3,-6)\), \(Y'(0,0)\), \(Z'(-1,-2)\)