Question

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

Answer 1

Answer:

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

Step-by-step 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 $(x,y)\rightarrow (x-7,y+5)$.

Answer 2

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)