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

**Solution:**

The coordinates of the point P(x, y) which divides the line segment joining the points A (x₁, y₁) and B(x₂, y₂), internally, in the ratio m₁_{ }: m₂ is given by the section formula: P (x, y) = [(mx₂ + nx₁)/m + n , (my₂ + ny₁)/m + n]

The coordinates of point A and B are (- 2, - 2) and (2, - 4) respectively.

AP = (3/7) AB

Hence, AB/AP = 7/3

We know that AB = AP + PB from figure,

Thus, AB/AP = 7/3 can be written as,

(AP + PB)/AP = (3 + 4)/3

1 + PB/AP = 1 + 4/3

PB/AP = 4/3

Therefore, AP : PB = 3 : 4

Point P(x, y) divides the line segment AB joining A(-2, -2) and B(2, -4) in the ratio 3:4. By using section formula,

P(x,y) = [(mx₂ + nx₁)/m + n , (my₂ + ny₁)/m + n]

P (x, y) = [(3 × 2 + 4 × (- 2))/(3 + 4) , (3 × (- 4) + 4 × (-2))/(3 + 4)]

= ((6 - 8)/7, (-12 - 8)/7)

= (-2/7, -20/7)

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 7

**Video Solution:**

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

NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 8

**Summary:**

If A and B are (- 2, - 2) and (2, - 4), respectively, then the coordinates of P such that AP = 3/7 AB and P lies on the line segment AB is (-2/7, -20/7).

**☛ Related Questions:**

- Find the coordinates of the point which divides the join of (- 1, 7) and (4, - 3) in the ratio 2: 3.
- Find the coordinates of the points of trisection of the line segment joining (4, - 1) and (- 2, - 3).
- To conduct Sports Day activities, in your rectangular-shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1m each. 100 flower pots have been placed at a distance of 1m from each other along with AD, as shown in Fig. 7.12. Niharika runs 1/4 th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segments joining the two flags, where should she post her flag?
- Find the ratio in which the line segment joining the points (- 3, 10) and (6, - 8) is divided by (- 1, 6).

visual curriculum