Question

notes kuta software - infinite pre - algebra translations of shapes 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 ii. for # 5 and 6, plot the figure first then do the translation. 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 rule

For a translation \(a\) units left or right and \(b\) units up or down, if a point \((x,y)\) is translated \(a\) units right (\(a>0\)) or left (\(a < 0\)) and \(b\) units up (\(b>0\)) or down (\(b < 0\)), the new - point is \((x + a,y + b)\).

Step2: Translate points for problem 1

Let's assume a point \((x,y)\) on the shape in problem 1. With a translation of 1 unit left (\(a=-1,b = 0\)), the new point is \((x-1,y)\). We apply this to each vertex of the shape to get the new - shaped vertices and then graph the new shape.

Step3: Translate points for problem 2

For a translation of 1 unit right (\(a = 1\)) and 2 units down (\(b=-2\)), for a point \((x,y)\) the new point is \((x + 1,y-2)\). Apply this to each vertex of the triangle in problem 2 and graph the new triangle.

Step4: Translate points for problem 3

For a translation of 3 units right (\(a = 3,b = 0\)), for a point \((x,y)\) the new point is \((x + 3,y)\). Apply to each vertex of the triangle in problem 3 and graph the new triangle.

Step5: Translate points for problem 4

Same as problem 2, for a translation of 1 unit right (\(a = 1\)) and 2 units down (\(b=-2\)), for a point \((x,y)\) the new point is \((x + 1,y-2)\). Apply to each vertex of the shape in problem 4 and graph the new shape.

Step6: Translate points for problem 5

Given points \(U(-3,-4)\), \(M(-1,-1)\), \(L(-2,-5)\) and a translation of 5 units up (\(a = 0,b = 5\)).
For point \(U\): \((-3,-4+5)=(-3,1)\)
For point \(M\): \((-1,-1 + 5)=(-1,4)\)
For point \(L\): \((-2,-5 + 5)=(-2,0)\)
Plot the original points, then the new points and graph the new shape.

Step7: Translate points for problem 6

Given points \(R(-4,-3)\), \(D(-4,0)\), \(L(0,0)\), \(F(0,-3)\) and a translation of 3 units up (\(a = 0,b = 3\)).
For point \(R\): \((-4,-3+3)=(-4,0)\)
For point \(D\): \((-4,0 + 3)=(-4,3)\)
For point \(L\): \((0,0 + 3)=(0,3)\)
For point \(F\): \((0,-3 + 3)=(0,0)\)
Plot the original points, then the new points and graph the new shape.

Since this is a set of graph - related translation problems, the actual answer is the set of new - graphed shapes which cannot be fully presented in text. But the general process for each problem is as described above for finding the new vertices and graphing. In a hand - written or graphing software context, you would follow the above steps to graph the translated shapes.

Answer:

Step1: Recall translation rule

For a translation \(a\) units left or right and \(b\) units up or down, if a point \((x,y)\) is translated \(a\) units right (\(a>0\)) or left (\(a < 0\)) and \(b\) units up (\(b>0\)) or down (\(b < 0\)), the new - point is \((x + a,y + b)\).

Step2: Translate points for problem 1

Let's assume a point \((x,y)\) on the shape in problem 1. With a translation of 1 unit left (\(a=-1,b = 0\)), the new point is \((x-1,y)\). We apply this to each vertex of the shape to get the new - shaped vertices and then graph the new shape.

Step3: Translate points for problem 2

For a translation of 1 unit right (\(a = 1\)) and 2 units down (\(b=-2\)), for a point \((x,y)\) the new point is \((x + 1,y-2)\). Apply this to each vertex of the triangle in problem 2 and graph the new triangle.

Step4: Translate points for problem 3

For a translation of 3 units right (\(a = 3,b = 0\)), for a point \((x,y)\) the new point is \((x + 3,y)\). Apply to each vertex of the triangle in problem 3 and graph the new triangle.

Step5: Translate points for problem 4

Same as problem 2, for a translation of 1 unit right (\(a = 1\)) and 2 units down (\(b=-2\)), for a point \((x,y)\) the new point is \((x + 1,y-2)\). Apply to each vertex of the shape in problem 4 and graph the new shape.

Step6: Translate points for problem 5

Given points \(U(-3,-4)\), \(M(-1,-1)\), \(L(-2,-5)\) and a translation of 5 units up (\(a = 0,b = 5\)).
For point \(U\): \((-3,-4+5)=(-3,1)\)
For point \(M\): \((-1,-1 + 5)=(-1,4)\)
For point \(L\): \((-2,-5 + 5)=(-2,0)\)
Plot the original points, then the new points and graph the new shape.

Step7: Translate points for problem 6

Given points \(R(-4,-3)\), \(D(-4,0)\), \(L(0,0)\), \(F(0,-3)\) and a translation of 3 units up (\(a = 0,b = 3\)).
For point \(R\): \((-4,-3+3)=(-4,0)\)
For point \(D\): \((-4,0 + 3)=(-4,3)\)
For point \(L\): \((0,0 + 3)=(0,3)\)
For point \(F\): \((0,-3 + 3)=(0,0)\)
Plot the original points, then the new points and graph the new shape.

Since this is a set of graph - related translation problems, the actual answer is the set of new - graphed shapes which cannot be fully presented in text. But the general process for each problem is as described above for finding the new vertices and graphing. In a hand - written or graphing software context, you would follow the above steps to graph the translated shapes.