Question

A sequence of translations maps ∆ABC to ∆A'B'C'. The vertices of ∆ABC are A(-3,5),B(7,8), and C(4,-9). The coordinates of A' are (2,2). What are the coordinates for B' and C'? Also, identify the translation rule used

Answer 1

The translation rule is
`(x,y)\to(x+5,y-3)`

`B'=(12,5)`

`C'=(-5,-12)`

Explanation:

The vertices of ∆ABC are A(-3,5),B(7,8), and C(4,-9).

The coordinates of A' are (2,2)

Let the translation vector be
`\binom{a}{b}`

Then we have
`\binom{-3}{5}+\binom{a}{b}=\binom{2}{2}`

`\implies \binom{-3+a}{5+b}=\binom{2}{2}`

`\implies -3+a=2\:,5+b=2`

`\implies a=2+3\:,b=2-5`

`\implies a=5\:,b=-3`

The translation rule is
`(x,y)\to(x+5,y-3)`

Therefore:

`B(7,8)\to(7+5,8-3)\to B'(12,5)`

`C(4,-9)\to(4+5,-9-3)\to C'(-5,-12)`