Question

The point M' (4,-5) is the result of a translation of 4 units left and 2 unitsup Usetranslation notation to describe the translation in the space below.

Answer 1

The point M' (4, -5) is the result of a translation of 4 units left and 2 units.

Recall that the rule for horizontal translation to the left is given by

$(x,y)\rightarrow(x-c,y)$

Where c is the number of units. (that is 4 units)

$\begin{gathered} x-c=4 \\ x-4=4 \\ x=4+4 \\ x=8 \end{gathered}$

So, this means that the x-coordinate of the pre-image was 8

Recall that the rule for vertical translation up is given by

$(x,y)\rightarrow(x,y+d)$

Where d is the number of units. (that is 2 units)

$\begin{gathered} y+d=-5 \\ y+2=-5 \\ y=-5-2 \\ y=-7 \end{gathered}$

So, this means that the y-coordinate of the pre-image was -7

The coordinates of the pre-image are

$M(8,-7)$

Finally, let us use translation notation to describe the translation.

$M(8,-7)\rightarrow(8-4,-7+2)=(4,-5)$