Question

if A and B are (-2, -2) and (2, -4) respectively. find the coordinates of P such that AP=3/7AB and P lies on the segment AB​

Answer 1

Coordinates of P = (–2/7 , –20/7)

Given Terms:

• Coordinate of A and B are (–2 , –2) and (2 , – 4) respectively.
• Also AP = 3/7AB.
• P lies on the segment AB.

Need To Find:

• What are the coordinates of point P ?

Solution: Let the coordinates be (x , y).

• Let P lies in the middle of line segment AB.
• P = (x , y)
• AB = AP + PB

• x¹ and y¹ = – 2 , – 2
• x² and y² = 2 , – 4

Solving the relation that is given between AP and AB.

➢ AP = 3/7AB

➢ 7AP = 3AB

➢ 7AP = 3 × (AP + PB)

➢ 7AP – 3AP = 3PB

➢ 4AP = 3PB

➢ AP/PB = 3/4

➢ AP : PB = 3 : 4

So point P divides the line segment AB in the ratio of 3 : 4.

➠ Section Formula =

• m1.x2 + m2.x1/m1 + m2
• m1.y2 + m2y1/m1 + m2
• where m1 and m2 = 3 and 4

➥ x = 3 × 2 + 4 × –2/3 + 4

➥ x = 6 – 8/7

➥ x = –2/7

and

➥ y = 3 × –4 + 4 × –2/7

➥ y = –12 – 8/7

➥ y = –20/7

Required coordinates of point P is (–2/7 , (–20/7)