Ok, so:
Let x and y be coordinate of the point C that partitions the segment.
And Let A = ( 2, -1 ) and B = ( 9 , 6 ).
So, given that C partitions the segment into a ratio of 5 to 2, we have:
Total parts of the segment: 5+2 = 7.
So, the point C is 5/7 of way from A to B.
Let me draw the situation:
Now, we know that the right distance is 7 and the upper distance is 7.
Now we multiply 5/7 per both distances.
5/7 * 7 = 5
5/7 * 7= 5
Now, we take the initial point A ( 2, -1 ), and sum 5 to each coordinate.
Then, the point C = ( 7 , 4 )
