Help please. Line segment AB¯¯¯¯¯¯¯¯ has endpoints A(−2,6) and B(4,−6). What are the coordinates of the point that partitions BA¯¯¯¯¯¯¯¯ according to the part-to-part ratio 2:4?

Question

Help pleae. geometry

Answer 1

2:4 means one part is 2/(2+4)=1/3 of AB and the other part is 2/3 of AB

Add 1/3 of the distance from -2 to 4. (1/3)(4+2)=2. -2+2=0 The x coordinate is 0

Subtract 1/3 of the distance from 6 to -6, (1/3)6+6)=4 6-4=2 The y coordinate is 2

The point is (0,2)

Check the answer

distance from (-2,6) to (0,2) is square root of (-2)^2 + (4)^2 = sqr20 = 2(5)^2

distance from (0,2) to (4,-6) is square root of (4)^2 +(8)^2 = sqr80 = 4(5)^2

First distance is half the 2nd distance, so the point divides AB into 2 parts in a ratio of 2:4