Question

Point A is at (6,1) and point C is at (2,-7)

Find the coordiantes of ppint b on line segamnt AC such that AB= 1/3BC

Answer 1

A (6. 1) C (2. -7)

6-2 = 4 1- (-7) = 8

as AB= 1/3 BC = AB= 1/4 AC

so x=6-4/4 =5

y= 1-8/4 =-1

so B(5, 1)

Answer 2

• B(5, - 1)

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Given

• Points A(6, 1) and C(2,- 7),
• Point B that partitions AC as AB : BC = 1 : 3.

Find point B

Use the section formula

• 
  `P=((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n) )`, where P- point to be found, m : n is the ratio and the (x,y) are coordinates of endpoints

Substitute and find the point B:

• 
  `B=((1*2+3*6)/(1+3) ,(1*(-7)+3*1)/(1+3) )=(20/4,-4/4)=(5,-1)`