Question

Find the values of x and y.
`T_(_-_2_,_7_)(x,y)=(3,-1)`

Answer 1

x = 5, y = -8

Explanation:

`T_((-2,\ 7))`

T - translation vector

(-2, 7) - coordinates of the vector

`T_((-2,\ 7))(x,\ y)=(3,\ -1)\to(x-2,\ y+7)=(3,\ -1)`

Therefore we have the equations:

`(1)\\x-2=3\qquad\text{add 2 to both sides}\\x-2+2=3+2\\x=5\\\\(2)\\y+7=-1\qquad\text{subtract 7 from both sides}\\y+7-7=-1-7\\y=-8`