Question

a four sided polygon with vertices (1, -2) (3, -1) (4, -4) (0, -5), find the new image 4 point leftward on the x axis and 2 points upward. in symbol (3pts)

Explanation:

Step1: Determine the translation rule

When a point \((x,y)\) is translated \(a\) units leftward on the \(x -\)axis and \(b\) units upward on the \(y -\)axis, the translation rule is \((x,y)\to(x - a,y + b)\). Here \(a = 4\) and \(b=2\).

Step2: Apply the translation rule to each vertex

• For the vertex \((1,-2)\):

Using the rule \((x,y)\to(x - 4,y + 2)\), we substitute \(x = 1\) and \(y=-2\).
\(x-4=1 - 4=-3\) and \(y + 2=-2+2 = 0\). So the new vertex is \((-3,0)\).

• For the vertex \((3,-1)\):

Substitute \(x = 3\) and \(y=-1\) into the rule. \(x-4=3 - 4=-1\) and \(y + 2=-1 + 2=1\). So the new vertex is \((-1,1)\).

• For the vertex \((4,-4)\):

Substitute \(x = 4\) and \(y=-4\) into the rule. \(x-4=4 - 4=0\) and \(y + 2=-4+2=-2\). So the new vertex is \((0,-2)\).

• For the vertex \((0,-5)\):

Substitute \(x = 0\) and \(y=-5\) into the rule. \(x-4=0 - 4=-4\) and \(y + 2=-5+2=-3\). So the new vertex is \((-4,-3)\).

Answer:

The new vertices of the polygon are \((-3,0)\), \((-1,1)\), \((0,-2)\), \((-4,-3)\)