Question

Write an algebraic rule to describe the translation C(5, –4) C’(–2, 1)

Answer 1

We can solve this by using the formula:
(x, y) (x + a, y + b) = (5,-4) (-2,1)

So, plugging in the values and solving for a and b,
5 + a = -2
a = -8

-4 + b = 1
b = 5

Therefore, the translation is
(x,y) (x - 8, y +5)

Answer 2

The required algebraic rule of translation is
`(x,y)\rightarrow (x-7,y+5)`.

Explanation:

The coordinates of a point are C(5, –4) and the coordinates of image are C’(–2, 1).

`C(5,-4)\rightarrow C'(-2,1)` .... (1)

Let the algebraic rule of translation is

`(x,y)\rightarrow (x+a,y+b)` .... (2)

From (1) and (2) we get

`x=5,y=-4`

`x+a=-2`

`5+a=-2`

`a=-2-5`

`a=-7`

The value of a is -7.

`y+b=1`

`-4+b=1`

`b=1+4`

`b=5`

The value of b is 5.

The algebraic rule of translation is

`(x,y)\rightarrow (x-7,y+5)`

Therefore the required algebraic rule of translation is
`(x,y)\rightarrow (x-7,y+5)`.