Question

xyz has vertices x(-4, -1), y(-2, -1) and z(-2, -5). give the coordinates for the image under the given translation: (x,y)→(x + 6,y + 5)
point (x,y) process
x (-4,-1)
y (-2,-1)
z (-2,-5)

Explanation:

Step1: Find new x - coordinate of X

For point X(-4, -1), use the translation rule \(x'=x + 6\). Substitute \(x=-4\) into the formula: \(x'=-4 + 6=2\).

Step2: Find new y - coordinate of X

Use the translation rule \(y'=y + 5\). Substitute \(y = - 1\) into the formula: \(y'=-1+5 = 4\). So \(X'(2,4)\).

Step3: Find new x - coordinate of Y

For point Y(-2, -1), use \(x'=x + 6\). Substitute \(x=-2\) into the formula: \(x'=-2 + 6=4\).

Step4: Find new y - coordinate of Y

Use \(y'=y + 5\). Substitute \(y=-1\) into the formula: \(y'=-1 + 5=4\). So \(Y'(4,4)\).

Step5: Find new x - coordinate of Z

For point Z(-2, -5), use \(x'=x + 6\). Substitute \(x=-2\) into the formula: \(x'=-2+6 = 4\).

Step6: Find new y - coordinate of Z

Use \(y'=y + 5\). Substitute \(y=-5\) into the formula: \(y'=-5 + 5=0\). So \(Z'(4,0)\).

Answer:

\(X'(2,4)\), \(Y'(4,4)\), \(Z'(4,0)\)