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.
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.
Let the coordinates of point P be (x, y).
The ratio in which P divides A(–1,7) and B(4,–3) is 2 : 3.
Using the section formula we have
\[x = \frac{4 \times 2 + 3 \times \left( - 1 \right)}{2 + 3} = \frac{8 - 3}{5} = 1\]
\[y = \frac{2 \times \left( - 3 \right) + 3 \times 7}{2 + 3} = \frac{- 6 + 21}{5} = 3\]
Thus, the coordinates of point P are (1, 3).
Explanation:-
Let P divide the line segment AB in the ratio 2:3, which means that AP is 2/5 of AB and BP is 3/5 of AB.
Let the coordinates of P be (x,y).
Then, we can use the section formula to find x and y.
For x-coordinate:
x = (3×2 – 2×1)/(3 + 2) (where x1 and x2 are the x-coordinates of A and B, respectively)
x = (3(4) – 2(-1))/5
x = (12 + 2)/5
x = 2.8
For y-coordinate:
y = (3y2 – 2y1)/(3 + 2) (where y1 and y2 are the y-coordinates of A and B, respectively)
y = (3(-3) – 2(7))/5
y = (-9 – 14)/5
y = -4.6
Therefore, the coordinates of point P are (2.8, -4.6).
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)