Question

What is the ratio in which the line 2x + 3y - 5= 0 divides the line
segment joining the points (8, -9) and (2, 1)?
A 8:1
B
7:2
с
7:6
D 2:5

Answer 1

Correct answer is:-

option a = 8:1

Answer:

In this given problem, the line of equation is 2x+3y−5=0 . Let A(x1,y1)=(8,−9) and B(x2,y2)=(2,1) be the end points of line segment AB and P(x,y) be the point of division of line segment joining the AB .

Let us assume that the ratio in which P divides AB is m:n=k:1 . Therefore, by using section formula coordinates of P is

P(x,y)=(mx2+nx1m+n,my2+ny1m+n)⇒P(x,y)=(2k+8k+1,k−9k+1)

We know that P lies on the line 2x+3y−5=0 .

Hence it will satisfy the equation of line.

Therefore, we can write

2(2k+8k+1)+3(k−9k+1)−5=0⇒2(2k+8k+1)+3(k−9k+1)=5

Now we take 1k+1 common in the left hand side of the equality sign and then multiplied both sides by k+1 . Then, we get

2(2k+8)+3(k−9)=5(k+1)

Let us simplify the above equation and find the value of k . Therefore, we can write

4k+16+3k−27=5k+5⇒4k+3k−5k=5+27−16⇒2k=16⇒k=162⇒k=8

Let us put k=8 in P(x,y)=(2k+8k+1,k−9k+1) .

Therefore, we get P(x,y)=(249,−19)

Therefore, we can say that the ratio in which the line 2x+3y−5=0 divided the line

segment joining the point (8,−9) and (2,1) is k:1=8:1 and coordinates of point P is given by (x,y)=(2k+8k+1,k−9k+1)=(249,−19) .

So, the correct answer is “ (249,−19) .”

Step-by-step explanation:

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