If A and B are two points having coordinates (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = AB.

Given points are A(-2, -2) and B(2, -4). Let P be (x, y)

Here given that AP = AB.

But AB = AP + BP

∴7AP = 3AB

7AP = 3(AP + BP)

∴4AP = 3BP

∴ =

By section formula,

x = , y =

For point P on AB, where m = 3 and n = 4

x = , y =

x = and y =

Hence, required coordinates is P( , )