If A (-14, -10), B(6, -2) is given, find the coordinates of the points which divide segment AB into four equal parts
If A (-14, -10), B(6, -2) is given, find the coordinates of the points which divide segment AB into four equal parts
Answer:-
Let P [left( x_1 , y_1 right)] and Q [left( x_2 , y_2 right)] divide the line AB into 3 equal parts.
AP = PQ = QB
[frac{AP}{PB} = frac{AP}{PQ + QB} = frac{AP}{AP + AP} = frac{AP}{2AP} = frac{1}{2}]
So, P divides AB in the ratio 1 : 2.
[x_1 = frac{1 times left( – 4 right) + 2 times 2}{2 + 1} = 0]
[ y_1 = frac{1 times left( – 8 right) + 2 times 7}{2 + 1} = 2]
[left( x_1 , y_1 right) = left( 0, 2 right)]
Also, [frac{AQ}{QB} = frac{AP + PB}{QB} = frac{QB + QB}{QB} = frac{2}{1}]
[x_2 = frac{2 times left( – 4 right) + 1 times 2}{2 + 1} = – 2]
[ y_2 = frac{2 times left( – 8 right) + 1 times 7}{2 + 1} = – 3]
[left( x_2 , y_2 right) = left( – 2, – 3 right)]
Thus, the coordinates of the point of intersection are
P [left( x_1 , y_1 right) = left( 0, 2 right)]
Q [left( x_2 , y_2 right)] =[left( – 2, – 3 right)]
Chapter 5. Co-ordinate Geometry – Practice Set 5.2 (Page 115)