Question

The point p divides the line segment AB joining points A(2,3) and B(4,5) in the ratio 3:4 does point p lie on the line 2x-3y+5=0

Answer 1

Answer:

the answer is in the picture plz see

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Answer 2

Question:

The point P divides the line segment AB joining points A(2,3) and B(4,5) in the ratio 3:4 does point P lie on the line 2x - 3y + 5 = 0.

Answer:

No.

Note:

• If the point P(x,y) divides the line joining the points A(x1,y1) and B(x2,y2) internally in the ratio m:n , then the co-ordinates of the point P will be ;

x = (m•x2 + n•x1)/(m + n)

y = (m•y2 + n•y1)/(m + n)

• If the point P(x,y) divides the line joining the points A(x1,y1) and B(x2,y2) externally in the ratio m:n , then the co-ordinates of the point P will be ;

x = (m•x2 - n•x1)/(m - n)

y = (m•y2 - n•y1)/(m - n)

• If a point lies on the line , then the coordinates of the point must satisfy the equation of the line .

Solution:

Let the coordinates of point P be (x,y) .

Now ,

It is given that the point P divides the line joining A(2,3) and B(4,5) in the ratio 3:4.

Clearly ,

x1 = 2

y1 = 3

x2 = 4

y2 = 5

m = 3

n = 4

Now,

The x-coordinate of point P(x,y) will be ;

=> x = (m•x2 + n•x1)/(m+n)

=> x = (3•4 + 4•2)/(3 + 4)

=> x = (12+8)/7

=> x = 20/7

Also,

The y-coordinate of point P(x,y) will be ;

=> y = (m•y2 + n•y1)/(m + n)

=> y = (3•5 + 4•3)/(3 + 4)

=> y = (15 + 12)/7

=> y = 27/7

Hence,

The point P is (20/7 , 27/7).

Now,

In order to check whether the point P(20/7,27/7) lies on line 2x - 3y + 5 = 0 , let's substitute the coordinates of point P in the equation of given line .

Thus,

Substituting x = 20/7 and y = 27/7 in the given equation 2x - 3y + 5 = 0 , we get ;

=> 2•(20/7) - 3•(27/7) + 5 = 0

=> 40/7 - 81/7 + 5 = 0

=> (40-81)/7 + 5 = 0

=> -41/7 + 5 = 0

=> (-41+35)/7 = 0

=> -6/7 = 0 { which is not true }

Since,

The point P(20/7,27/ 7) doesn't satisfy the equation of line , hence it doesn't lie on the line.