Given A(4,-3), B(8,5). Find the coordinates of the point that divides segment AB in the ratio 3:1.
17. Given A(4,-3), B(8,5). Find the coordinates of the point that divides segment AB in the ratio 3:1.
Solution
Let the coordinate of the point which divide the line AB in the ratio 3 : 1 be P(a, b)
[a = frac{3 times 8 + 1 times 4}{3 + 1} = frac{24 + 4}{4} = 7]
[b = frac{3 times 5 + 1 times left( – 3 right)}{3 + 1} = frac{15 – 3}{4} = 3]
P(a, b) = (7, 3)
Explanation:-
The question asks to find the coordinates of the point P which divides the line segment AB in the ratio 3:1. Let the coordinates of point P be (a, b).
To find the value of a, we use the formula for finding a point that divides a line segment in a given ratio:
a = (3x-coordinate of point B + 1x-coordinate of point A) / (3+1) = (38 + 14) / (3+1) = (24 + 4) / 4 = 7
To find the value of b, we use the same formula:
b = (3y-coordinate of point B + 1y-coordinate of point A) / (3+1) = (35 + 1(-3)) / (3+1) = (15 – 3) / 4 = 3
Therefore, the coordinates of point P are (7, 3).
Chapter 5. Co-ordinate Geometry – Problem set 5 (Page 122)