find the coordinates of the point which devides the line segment from (-2,1) and (2,-3) in the ratio 3 is to 4.

Question

find the coordinates of the point which devides the line segment from (-2,1) and (2,-3) in the ratio 3 is to 4.

 

 

Answer 1

A = (x_A,y_A) = (-2,1)

B = (x_B,y_B) = (2,-3)

 

Let point P represent the point on AB such that AP:PB = 3:4.  In a ratio of 3:4, you are dividing the line into 3+4 = 7 parts.  Line AP is 3/7 of AB, line PB is 4/7 of AB.  Since we want AP = 3/7 of AB, we use the ratio r = 3/7.  The formula for point P is:

 

P = (x_P,y_P) = ( x_A+r(x_B-x_A), y_A+r(y_B-y_A) )

 

P = (-2+(3/7)(2 - -2), 1+(3/7)(-3 - 1))

 

p = (-2+12/7, 1-12/7)

 

p = (-2/7, -5/7)