# Let #A(x_a,y_a)# and #B(x_b,y_b)# be two points in the plane and let #P(x,y)# be the point that divides #bar(AB)# in the ratio #k :1#, where #k>0#. Show that #x= (x_a+kx_b)/ (1+k)# and #y= (y_a+ky_b)/( 1+k)#?

##### 1 Answer

Nov 18, 2016

See proof below

#### Explanation:

Let's start by calculating

We start with the

Multiplying and rearranging

Solving for

Similarly, with the