Question

Write a translation rule that maps point D(7,-3) onto point D'(2,5).

Answer 1

We are given D (7, -3) and D'(2, 5).

SAppy the transformation
D'(x,y) → D(x-5, y+8).
Then 
x=7 → x=7-5 = 2
y=-3 → y=-3+8 = 5

Answer: D (x-5, y+8) → D'

Answer 2

ANSWER

The translation rule is

$D(x,y)\rightarrow D'(x-5,y+8).$

EXPLANATION

Let $\binom{x}{y}$
be the translation vector that maps $D(7,-3)$
on to $D'(2,5)$.

Then we have the vector equation,

$\binom{7}{ - 3} + \binom{x}{y} = \binom{2}{5}$

We now solve for
$\binom{x}{y}$

$\binom{x}{y} = \binom{2}{5} - \binom{7}{ - 3}$

This simplifies to,

$\binom{x}{y} = \binom{2 - 7}{5 - - 3}$

$\binom{x}{y} = \binom{2 - 7}{5 + 3}$

$\binom{x}{y} = \binom{ - 5}{8}$

Therefore the translation rule is,

$D(x,y)\rightarrow D'(x-5,y+8)$