Question

The point p divides the line segment AB joining points A(3,4) and B(6,7) in the ratio 1:2 does point p lie on the line x-4y+10=0

Answer 1

Question:

The point P divides the line segment AB joining points A(3,4) and B(6,7) in the ratio 1:2 does point P lie on the line x - 4y + 10 = 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(3,4) and B(6,7) in the ratio 1:2.

Clearly ,

x1 = 3

y1 = 4

x2 = 6

y2 = 7

m = 1

n = 2

Now,

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

=> x = (m•x2 + n•x1)/(m+n)

=> x = (1•6 + 2•3)/(1 + 2)

=> x = (6+6)/3

=> x = 12/3

=> x = 4

Also,

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

=> y = (m•y2 + n•y1)/(m + n)

=> y = (1•7 + 2•4)/(1 + 2)

=> y = (7 + 8)/3

=> y = 15/3

=> y = 5

Hence,

The point P is (4,5).

Now,

In order to check whether the point P(4,5) lies on the line x - 4y + 10 = 0 , let's substitute the coordinates of point P in the equation of given line .

Thus,

Substituting x = 4 and y = 5 in the given equation x - 4y + 10 = 0 , we get ;

=> 4 - 4•5 + 10 = 0

=> 4 - 20 + 10 = 0

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

Since,

The point P(4,5) doesn't satisfy the equation of line , hence it doesn't lie on the line.