Try this:
var point_a = [0, 0];
var point_b = [100, 200];
var coord = [50, 100];
function checkCoordinate(coord) {
var slope = (point_b[1] - point_a[1]) / (point_b[0] - point_a[0]);
var newSlope = (point_b[1] - coord[1]) / (point_b[0] - coord[0]);
if (coord[0] > point_a[0] && coord[0] < point_b[0] && coord[1] > point_a[1] && coord[1] < point_b[1] && slope == newSlope) {
alert('Yes! they are in the same line.');
} else {
alert('No :/');
}
}
checkCoordinate(coord);