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Question
Find the coordinates of point P if P divides the line segment joining the points A(–1, 7) and B(4, –3) in the ratio 2 : 3.
Solution
Let (x1, y1) = (–1, 7) and (x2, y2) = (4, –3), m : n = 2 : 3.
According to the section formula,
`x = (mx_2 + nx_1)/(m + n)`
`x = (2 × 4 + 3 × (–1))/(2 + 3)`
`x = (8 – 3)/5`
`x = 5/5`
∴ `x = 1`
`y = (my_2 + ny_1)/(m + n)`
`y = (2 × (–3) + 3 × 7)/(2 + 3)`
`y = (–6 + 21)/(5)`
`y = (15)/(5)`
∴ y = 3
∴ The coordinate of points p is (1, 3).
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= `((x_1 + x_2)/2, (y_1+ y_2)/2)`
= `(square/2, square/2)`
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∴ Coordinates of the midpoint = `(2, square)`
If A(5, 4), B(–3, –2) and C(1, –8) are the vertices of a ∆ABC. Segment AD is median. Find the length of seg AD:
Point M (2, b) is the mid-point of the line segment joining points P (a, 7) and Q (6, 5). Find the values of ‘a’ and ‘b’.
Find the coordinates of the mid-point of the line segment with points A(– 2, 4) and B(–6, –6) on both ends.
Find the coordinates of point P where P is the midpoint of a line segment AB with A(–4, 2) and B(6, 2).
Solution :
Suppose, (–4, 2) = (x1, y1) and (6, 2) = (x2, y2) and co-ordinates of P are (x, y).
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∴ Co-ordinates of midpoint P are `square`.
