Question

The vector (-3,2) describes the translations A(-1, x) —- A’(-4y, 1) and B (2z-1, 1) —- B’(3,3) Find the value of x, y and z.

Answer 1

Given:

The vector (-3,2) describes the translations:

`\begin{gathered} A(-1,x)\rightarrow A^(\prime)(-4y,1) \\ B(2z-1,1)\rightarrow B^(\prime)(3,3) \end{gathered}`

From the first translation, we will find the values of (x) and (y)

So, we have the rule:

`(-1,x)+(-3,2)=(-4y,1)`

The sum of the x-coordinates from the left will equal the x-coordinates from the right

`-1-3=-4y`

Solve the equation to find y

`\begin{gathered} -4=-4y\rightarrow(/-4) \\ y=1 \end{gathered}`

Now, The sum of the y-coordinates from the left will equal the y-coordinates from the right

`x+2=1`

Subtract 2 from both sides:

`x=-1`

From the second translation, we will find the value of z:

`\begin{gathered} (2z-1,1)+(-3,2)=(3,3) \\ 2z-1-3=3 \\ 2z-4=3 \\ 2z=3+4 \\ 2z=7 \\ z=(7)/(2)=3.5 \end{gathered}`

so, the answer will be:

`\begin{gathered} x=-1 \\ y=1 \\ z=3.5 \end{gathered}`

See the following figure: