Question

Draw the image of AABC after a translation 3 units right and 1 unit down and a reflection across the y-axis.

Answer 1

In order to calculate the coordinates of the points after a translation of 3 units right and 1 unit down, let's add 3 units to the x-coordinate and decrease 1 unit from the y-coordinate of all points.

So we have:

`\begin{gathered} A(-4,2)\to A^(\prime)(-4+3,2-1)=A^(\prime)(-1,1) \\ B(-6,3)\to B^(\prime)(-6+3,3-1)=B^(\prime)(-3,2) \\ C(-5,6)\to C^(\prime)(-5+3,6-1)=C^(\prime)(-2,5) \end{gathered}`

Then, to calculate the coordinates after a reflection across the y-axis, let's change the signal of the x-coordinate of all points.

So we have:

`\begin{gathered} A^(\prime)(-1,1)\to A^(\doubleprime)(1,1) \\ B^(\prime)(-3,2)\to B^(\doubleprime)(3,2) \\ C^(\prime)(-2,5)\to C^(\doubleprime)(2,5) \end{gathered}`

Drawing the resulting triangle, we have: