Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts
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.
By observation, points P, Q, R divides the line segment A (- 2, 2) and B (2, 8) into four equal parts.
Point P divides the line segment AQ into two equal parts.
Therefore, AP : PB is 1 : 3
Using section formula which is given by P (x, y) = [(mx₂ + nx₁) / m + n , (my₂ + ny₁) / m + n]
Hence, coordinates of P = [(1 × 2 + 3 × (- 2)) / (3 + 1), (1 × 8 + 3 × 2) / (3 + 1)] = (- 1, 7/2)
Point Q divides the line segment AB into two equal parts
Using mid point formula,
Q = [(2 + (- 2)) / 2, (2 + 8) / 2] = (0, 5)
Point R divides the line segment BQ into two equal parts
Coordinates of R = [(2 + 0) / 2, (8 + 5) / 2] = (1, 13/2)
☛ Check: NCERT Solutions for Class 10 Maths Chapter 7
Video Solution:
Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts
NCERT Class 10 Maths Solutions Chapter 7 Exercise 7.2 Question 9
Summary:
The coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts is (- 1, 7/2), (0, 5), and (1, 13/2).
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