1) 2x - 3y - 50 2) 3x - 4y + 40 = 0 3) x + 3y - 5 = 0 4) 20x + 25y - 71 = 0
15 The equation of the straight line whose slope - 2/3 and which divides the line seg-
ment joining (3.-4), (7, 2) in the ratio 3 : 2 externally is
1) 2x + 3y - 12 = 0 2) 3x + 2y + 270 3) 2x + 3y + 29 = 0 4) 2x + 3y - 72 = 0
16. If (2,-2).(-1,2), (3,5) are the vertices of a triangle then the equation of the side not
passing through (2,-2) is
1) x + 2y + 10 2) 2x - y - 4 = 0 3) x-3y-30 4) 3x – 4y + 11-0
17. The equations of the medians of the triangle with vertices (0.-1).(-2,0).(- 1. - }) are
1) x + 2y + 1 = 0,*+ 1 = 0, x - 2y + 1 = 0 2)x+ 2y + 3 = 0,2x - 4y +9=0.2x - y-4=0
3) r - 3y - 3 -0.x + 1 = 0,4x + 3y + 8 = 0
4) 4x + 3y - 2 - 0,3x - 4y + 11 = 0,7x - y - 16 = 0
18. The vertices of a triangle ABC are A (1, 1), B (-3,4), C (2,-5). The equation to the
altitude through the vertex A is
1) 5x+y+4=0 2) 5x + 9y - 4 - 0 3) 5x - 9y + 4 = 0 4) Sx - 9y4=0
19. The equation to the perpendicular bisector of the line segment joining (1,2).(-3, 4) is
1) 2x - y + 5 = 0 2) 3x - 5y + 4 = 0 3) 3x - Sy- 10 = 0 4x + y - 40
20. The equation of the line passing through the point (-2,3) and parallel to
3x - 4y + 7 = 0 is
1) 3x + 4y +18=0 2) 3x + 4y - 18 = 0 3) 3x - 4y+ 18 = 0 4) 3x - 4y - 18 = 0
Answers
Step-by-step explanation:
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 ±45
∘
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 bisectors of angle between given lines and they pass through ( 1, 2)
∴ y - 2 = m ( x - 1)
where m is slope of any of bisectors given by
5
3x+4y−5
=±
5
4x−3y−15
or x - 7y + 13 = 0 or 7x + y - 20 = 0
∴ m = 1 / 7 or - 7
putting in (1) , the required lines are 7x + y - 9 = 0
and x - 7y + 13 = 0 as found above
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