add columns of list {a0,b0} to columns of list {{a0,b0} ,{a1,b1} ,{a2,b2} ...{ax,bx} }

Question

If I want to add the columns of {1,2} to each of the columns of say

{{1,2},{3,2},{4,2}}

resulting in

{{2, 4}, {4, 4}, {5, 4}}

How would I do this? and for any given number of rows?

{{1,2},{3,2}...{x,y}}

Answer 1

Every time anyone says "I want to do x to every item in a list" think Map

m={{1,2},{3,2},{4,2}};
Map[#+{1,2}&,m]

which returns

{{2,4},{4,4},{5,4}}

If that # and & stuff is too confusing then you can do the same by writing your own function

m={{1,2},{3,2},{4,2}};
f[v_]:=v+{1,2};
Map[f,m]

which returns

{{2,4},{4,4},{5,4}}

Answer 2

Another way.

pts = {{1, 2}, {3, 2}, {4, 2}};
TranslationTransform[First@pts] /@ pts

pts = {{1, 2}, {3, 2}, {4, 2}};
ConstantArray[{1, 0, 0}, Length@pts] . pts + pts

{{2, 4}, {4, 4}, {5, 4}}

Answer 3

Two (of probably very many) ways:

data//With[{x = #[[1]]},ArrayReduce[x+#&,#,2]]&
(* {{2, 4}, {4, 4}, {5, 4}} *)

or

data//With[{x = #[[1]]},x+#&/@#]&

where

data ={{1,2},{3,2},{4,2}}

Edit

Add a column to all columns (see this answer by Carl Woll)

addColToAll[mat_,col_] := With[{x=col},mat.SparseArray[{{x,x}->2,Band[{1, 1}]->1,
    {x,_}->1},Dimensions[mat][[2]]]]

Add a row to all rows:

addRowToAll[mat_,row_] := With[{x=row},Transpose[mat].SparseArray[{{x,x}->2,Band[{1, 1}]->1,{x,_}->1},Dimensions[mat][[1]]]//Transpose]

Examples

addRowToAll[data,1]
(* {{2, 4}, {4, 4}, {5, 4}} *)
addRowToAll[data,2]
(* {{4, 4}, {6, 4}, {7, 4}} *)
addRowToAll[data,3]
(* {{5, 4}, {7, 4}, {8, 4}}
addColToAll[data,1]
(* {{2, 3}, {6, 5}, {8, 6}} *)
data
(* {{1, 2}, {3, 2}, {4, 2}}  *)