Q1)find the ratio in which the line 2x + 3y- 5 = 0 divides the line segment joining the points (8,-9) and (2,1).Also, find the coordinates of the points of division.
Q2)find the ratio in which the line 2x + 3y- 5 = 0 divides the line segment joining the points (8,-9) and (2,1).Also, find the coordinates of the points of division.
Answers
HEY MATE I HAVE ANSWERED UR QUERY PLEASE MARK AS BRAINLIEST AND GIVE IT A THANKS PLEASE BROTHER.......
Let the line 2x+3y−5=0 divides the line segment joining the points A (8,-9) and B (2,1) in the ratio λ:1 at point P.
∴ Coordinates of P ≡{2λ+8λ+1,λ−9λ+1}
[∵ internal division ={m1x2+m2x1m1+m2,m1y2+m2y1m1+m2}]
But P lies on 2x+3y−5=0.
∴2(2λ+8λ+1)+3(λ−9λ+1)−5=0
⇒2(2λ+8)+3(λ−9)−5(λ+1)=0
⇒4λ+16+3λ−27−5λ−5=0
⇒2λ−16=0
⇒λ=8λ⇒λ:1=8:1
So , the point P divised the line in the ratio 8:1 .
∴ Point of division P ≡{2(8)+88+1,8−98+1}
≡(16+89,−19)
≡(249,−19)≡(83,−19)
Hence , the required point of division is (83,−19).
Answer:
Let the line 2x+3y−5=0 divides the line segment joining the points A (8,-9) and B (2,1) in the ratio λ:1 at point P.
∴ Coordinates of P ≡{2λ+8λ+1,λ−9λ+1}
[∵ internal division ={m1x2+m2x1m1+m2,m1y2+m2y1m1+m2}]
But P lies on 2x+3y−5=0.
∴2(2λ+8λ+1)+3(λ−9λ+1)−5=0
⇒2(2λ+8)+3(λ−9)−5(λ+1)=0
⇒4λ+16+3λ−27−5λ−5=0
⇒2λ−16=0
⇒λ=8λ⇒λ:1=8:1
So , the point P divised the line in the ratio 8:1 .
∴ Point of division P ≡{2(8)+88+1,8−98+1}
≡(16+89,−19)
≡(249,−19)≡(83,−19)
Hence , the required point of division is (83,−19).
Step-by-step explanation: