Question

if two lines 3x+4y+5 =0 and 4x+y+3=0 divisible internally at the ratio 1:2​

Answer 1

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• The given lines are perpendicular and as AB = AC , Therefore △ ABC is art . angled isosceles .

• Hence the line BC through ( 1 ,2) will make an angles of ±45degree with the given lines .

• Its equations is y - 2 = m (x - 1) where m = 1 / 7 and -7 as in .Hence the possible equations are 7x + y - 9 = 0 and x - 7y + 13 = 0

• Alt :

The two lines will be parallel to bi sect ors of angle be.tween given lines and they pas through ( 1, 2)

∴ y - 2 = m ( x - 1)

where m is slope of any of bi sect ors given by

3x + 4y − 5 up.on 5 = ± 4x−3y−15 u.pon 5

or x - 7y + 13 = 0 or 7x + y - 20 = 0

• ∴ m = 1 / 7 or - 7

1. puting in (1) , the req.uired lines are

7x + y - 9 = 0

• and x - 7y + 13 = 0 as found above

hope it helps uh babe!

Answer 2

Answer: The point of intersection of the two lines is (8, -11/4).

Step-by-step explanation:

The condition for two lines to be divisible internally in the ratio 1:2 is that they intersect, and the point of intersection lies on the segment joining the two points of intersection.

To find the point of intersection of the two lines, we can substitute one equation into the other to eliminate one of the variables. For example, using the first equation, we can solve for y:

3x + 4y + 5 = 0

4y = -3x - 5

y = -3/4 x - 5/4

Substituting this into the second equation:

4x + (-3/4 x - 5/4) + 3 = 0

7x/4 = 8/4

x = 8

Substituting x = 8 back into the equation for y, we find that:

y = -3/4 x - 5/4 = -3/4 * 8 - 5/4 = -11/4

The point of intersection of the two lines is (8, -11/4). To check if it lies on the segment joining the two points of intersection, we find the two points of intersection and check if the point (8, -11/4) lies between them.

Note: Since the two lines are parallel, they do not intersect and the point of intersection is not defined, therefore the answer is that they cannot be divided internally in the ratio 1:2.