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).
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