# 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 (x_{1}, y_{1}) and B(x_{2}, y_{2}), internally, in the ratio m_{1 }: m_{2} is given by the section formula: P (x, y) = [mx_{2} + nx_{1}/m + n , my_{2} + ny_{1}/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,

(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 in the ratio 3:4. By using section formula, we get

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)

**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:

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

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)