On the abscissa axis find a point equidistant from points M (-4; -2) and N (6; 4)

Point C (x; 0) is a point on the X axis, equidistant from these points.

CM = CN

CM ^ 2 = (-4 – x) ^ 2 + (-2 – 0) ^ 2 = 16 + 8x + x ^ 2 + 4 = x ^ 2 + 8x + 20

СN ^ 2 = (6 – x) ^ 2 + (4 – 0) ^ 2 = 36 – 12x + x2 ^ + 16 = x ^ 2 – 12x + 52

x ^ 2 + 8x + 20 = x ^ 2 – 12x + 52

20x = 32

x = 32: 20

x = 1.6

С (1,6; 0) -search point