f[x_,y_] := x^2 + y^2

ContourPlot[f[x, y],
{x, -2, +2},
{y, -2, +2}
]

f[1,-1]
f[1,+1]
f[2,+1]

m = {0.5, -1}

0.5 * m + 0.5 * {1, 1}

f[0.75, 0]

{0.75,0}
{0, -1}
{1,-1}

f[0.75, 0]
f[0, -1]
f[1, -1]

m = 1/2({0.75, 0} + {0, -1})

1/2 m - 1/2 {1, -1}

f[0.375, -1/2]

m =1/2( {-0.3125`,(1/4)} + {0.75, 0})

1/2 m - 1/2 {0, -1}

f[0.109375, 9/16]

f[-0.3125,0.25]
f[0.75,0]
f[0, 1]