# Evaluating “Table” expression with only sequential combination of parameter values

I need to make a list by evaluating

{1, x, y, x*y}


on a sequence of points

{-10,10},{10,10},{10,-10},{-10, -10}


Neither

Table[{1, x, y, x*y}, {y, 10, -10, -20}, {x, -10, 10, 20}]


nor

Table[{1, x, y, x*y}, {y, {10, 10, -10, -10}}, {x, {-10, 10, 10, -10}}]


gave me the desired result.

I expect the result to be:

{{1, -10, 10, -100}, {1, 10, 10, 100}, {1, 10, -10, 100}, {1, -10, -10, -100}}


Is there a way to do it with Table? Thanks.

• ricecakebear, thinking that it is a typo, I changed {-10,10} in the last entry of your set of points to {-10, -10}. If it is not a typo and it should stay {-10,10} please let me know, I will roll back my edit. – kglr Sep 11 '17 at 6:33
• @kglr Yeah, it's a typo. Thanks for correction. – ricecakebear Sep 11 '17 at 6:49

ClearAll[f]
f[{x_, y_}] := {1, x, y, x*y}

f /@ {{-10, 10}, {10, 10}, {10, -10}, {-10, -10}}


{{1, -10, 10, -100}, {1, 10, 10, 100}, {1, 10, -10, -100}, {1, -10, -10, -100}}

Table[f[i], {i, {{-10, 10}, {10, 10}, {10, -10}, {-10, -10}}}]


{{1, -10, 10, -100}, {1, 10, 10, 100}, {1, 10, -10, -100}, {1, -10, -10, -100}}

Or

Table[{1, i[[1]], i[[2]], i[[1]] i[[2]]},
{i, {{-10, 10}, {10, 10}, {10, -10}, {-10, -10}}}]


{{1, -10, 10, -100}, {1, 10, 10, 100}, {1, 10, -10, -100}, {1, -10, -10, -100}}