Question

what are the coordinates of the point on the directed line segment from (2,-1) to (9,6) that partitions the segment into a ratio of 5 to 2

Answer 1

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 )