Question related to coordinate geometry.Finding the ratio
Determine the ratio in which the line 2x + y-4 = 0 divides the line segment joining the points A (2, – 2) and B( 3,7)
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Question related to coordinate geometry.Finding the ratio
In 2:9 ratio the line 2x+y-4=0 divides the line segment joining A(2,-2) & B(3,7)
Explanation: Assume, the line 2x+y-4=0 divides line segment AB in the ratio k:1 at point P(X, Y)
Then P coordinates are :
X co-ordinates of P = Px= (3*k+1*2)/(k+1) = (3k+2)/(k+1)
Y co-ordinates of P = Py= (7*k+1*-2)/(k+1) = (7k-2)/(k+1)
As P passes through line 2x+y-4=0
Put P(X,Y) in the line:
k:1 = 2/9 : 1 = 2:9
∴ In 2:9 ratio point P divides AB.