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
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)