Question

graph the image of the figure using the transformation given. 1) translation: 1 unit left 2) translation: 1 unit right and 2 units down 3) translation: 3 units right 4) translation: 1 unit right and 2 units down 5) translation: 5 units up u(-3, -4), m(-1, -1), l(-2, -5) 6) translation: 3 units up r(-4, -3), d(-4, 0), l(0, 0), f(0, -3)

Explanation:

Step1: Recall translation rules

For a translation \(a\) units right and \(b\) units down, the transformation for a point \((x,y)\) is \((x + a,y - b)\). For \(a\) units right and \(b = 0\) (no vertical change), \((x,y)\to(x + a,y)\) and for \(b\) units up (\(a=0\)), \((x,y)\to(x,y + b)\).

Step2: Translate each point for problem 1

Since no specific points are given for problem 1 in text - assume we have points on the shape. For each point \((x,y)\) of the original shape, if we want to translate it 1 unit right and 2 units down, the new point is \((x + 1,y-2)\). Plot these new - points to get the translated shape.

Step3: Translate each point for problem 2

For each point \((x,y)\) of the original shape, the new point after translation 1 unit right and 2 units down is \((x + 1,y - 2)\). Plot the new points to graph the translated figure.

Step4: Translate each point for problem 3

For a point \((x,y)\) of the original shape, after a translation of 3 units right, the new point is \((x+3,y)\). Plot the new - points to get the translated shape.

Step5: Translate each point for problem 4

For each point \((x,y)\) of the original shape, the new point after translation 1 unit right and 2 units down is \((x + 1,y - 2)\). Plot the new points to graph the translated figure.

Step6: Translate each point for problem 5

Given points \(U(-3,-4)\), \(M(-1,-1)\), \(L(-2,-5)\). After a translation of 5 units up, the new points are \(U'(-3,-4 + 5)=(-3,1)\), \(M'(-1,-1 + 5)=(-1,4)\), \(L'(-2,-5 + 5)=(-2,0)\). Plot these new points to get the translated shape.

Step7: Translate each point for problem 6

Given points \(R(-4,-3)\), \(D(-4,0)\), \(L(0,0)\), \(F(0,-3)\). After a translation of 3 units up, the new points are \(R'(-4,-3 + 3)=(-4,0)\), \(D'(-4,0 + 3)=(-4,3)\), \(L'(0,0 + 3)=(0,3)\), \(F'(0,-3 + 3)=(0,0)\). Plot these new points to get the translated shape.

Since this is a graph - based problem, the final answer is the set of new - plotted shapes on the coordinate plane for each of the given translations. But as we are in a text - based format, the general method to get the answer is as described above for each of the 6 translation problems.

Answer:

Step1: Recall translation rules

For a translation \(a\) units right and \(b\) units down, the transformation for a point \((x,y)\) is \((x + a,y - b)\). For \(a\) units right and \(b = 0\) (no vertical change), \((x,y)\to(x + a,y)\) and for \(b\) units up (\(a=0\)), \((x,y)\to(x,y + b)\).

Step2: Translate each point for problem 1

Since no specific points are given for problem 1 in text - assume we have points on the shape. For each point \((x,y)\) of the original shape, if we want to translate it 1 unit right and 2 units down, the new point is \((x + 1,y-2)\). Plot these new - points to get the translated shape.

Step3: Translate each point for problem 2

For each point \((x,y)\) of the original shape, the new point after translation 1 unit right and 2 units down is \((x + 1,y - 2)\). Plot the new points to graph the translated figure.

Step4: Translate each point for problem 3

For a point \((x,y)\) of the original shape, after a translation of 3 units right, the new point is \((x+3,y)\). Plot the new - points to get the translated shape.

Step5: Translate each point for problem 4

For each point \((x,y)\) of the original shape, the new point after translation 1 unit right and 2 units down is \((x + 1,y - 2)\). Plot the new points to graph the translated figure.

Step6: Translate each point for problem 5

Given points \(U(-3,-4)\), \(M(-1,-1)\), \(L(-2,-5)\). After a translation of 5 units up, the new points are \(U'(-3,-4 + 5)=(-3,1)\), \(M'(-1,-1 + 5)=(-1,4)\), \(L'(-2,-5 + 5)=(-2,0)\). Plot these new points to get the translated shape.

Step7: Translate each point for problem 6

Given points \(R(-4,-3)\), \(D(-4,0)\), \(L(0,0)\), \(F(0,-3)\). After a translation of 3 units up, the new points are \(R'(-4,-3 + 3)=(-4,0)\), \(D'(-4,0 + 3)=(-4,3)\), \(L'(0,0 + 3)=(0,3)\), \(F'(0,-3 + 3)=(0,0)\). Plot these new points to get the translated shape.

Since this is a graph - based problem, the final answer is the set of new - plotted shapes on the coordinate plane for each of the given translations. But as we are in a text - based format, the general method to get the answer is as described above for each of the 6 translation problems.