urgent math help please help

Question

Points A, B and C are collinear such that AB:BC = 2:3. Point A is located at (2,3) and Point C is located (8,12).

Find B(x,y) and the Midpoint M given the endpoints. 

(Hint: Draw a picture). Write both as an ordered pair with no spaces and as decimals if needed.

B =    

M =    

Answer 1

For point B the ratio of the lengths of each line segment must be 2 : 3. The total x change is ( 8 - 2) = 6 and the total y change is ( 12 - 3) = 9. The ratio of 2 : 3 means there are 5 parts; 2 of the 5 parts are in AB and 3 of the 5 parts are in BC. Multiply the part size times the total change and add to the original point.

For B X = 2/5 of 6 or 0.4 times 6 or 2.4 . Now add to the original 2 : 2.4+ 2 = 4.4

Or going from the C end x = 3/5 of 6 or 0.6 times 6 or 3.6 . Now go down from 8 - 3.6 = 4.4

Do the same for Y = 2/5 of 9 or 0.4 times 9 = 3.6. Now add to the original 3.6 + 3 =6.6

Or going from the C end 3/5 of 9 or 0.6 times 9 = 5.4. Now subtract from the C end for 12 - 5.4 = 6.6

B = ( 4.4, 6.6)

For the point M the values are the average of each. For x: ( 2+8)/2 = 5 and for y: ( 3 + 12)/2 = 7.5

M = ( 5, 7.5)