In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a: b. P(-3, 7), Q(1, -4), a : b = 2: 1
2. In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a: b. P(-3, 7), Q(1, -4), a : b = 2: 1
Answer:-
Let the coordinates of point A be (x, y).
P(–3, 7), Q(1, –4), a : b = 2 : 1
Using section formula
[x = frac{2 times 1 + 1 times left( – 3 right)}{2 + 1} = frac{2 – 3}{3} = frac{- 1}{3}]
[y = frac{2 times left( – 4 right) + 1 times 7}{2 + 1} = frac{- 8 + 7}{3} = frac{- 1}{3}]
[left( x, y right) = left( frac{- 1}{3}, frac{- 1}{3} right)]
Answer:-
Let the co-ordinates of point A be (x, y).
By the section formula,
x = (b * x1 + a * x2)/(a + b) y = (b * y1 + a * y2)/(a + b)
Here, x1 = -3, y1 = 7, x2 = 1, y2 = -4, a = 2, b = 1.
Substituting the values, we get:
x = (1 * (-3) + 2 * 1) / (2 + 1) = -1/3 y = (1 * 7 + 2 * (-4)) / (2 + 1) = -1/3
Therefore, the co-ordinates of point A are (-1/3, -1/3).
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)