Home
Class 12
MATHS
The number of triangles that the four li...

The number of triangles that the four lines `y = x + 3, y = 2x + 3, y = 3x + 2,` and `y + x = 3` form is (a) 4 (b) 2 (c) 3 (d) 1

A

4

B

2

C

3

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
The lines y=x+3, y=2x+3 and y+x=3 are concurrent at (0,3).
Rough sketch of the lines is as shown in the figure.

From the figure, three triangles ABD, ABC nad ACD can be formed.
Promotional Banner

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (MULTIPLE CORRECT ANSWERS TYPE)|30 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise EXERCISE (LINKED COMPREHENSION TYPE)|27 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.6|5 Videos

  • STRAIGHT LINE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|8 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise JEE ADVANCED (Numerical Value Type )|1 Videos

Similar Questions

Explore conceptually related problems

The circumcenter of the triangle formed by the line y=x ,y=2x , and y=3x+4 is

The triangle formed by the lines x+y =0,3x+y=4 and x+3y=4 is-

The triangle formed by the line x+sqrt3y=0, x- sqrt3y=0 and x=4 is-

The orthocentre of the triangle formed by the lines x+y=1,2x+3y=6 and 4x-y+4=0 lies in

If the three straight lines y = 3x- 1, 2y = x + 3 and 3y - 4 = mx are concurrent, then find the value of m.

Find the circumcentre and circumradius of the triangle formed by the lines 3y - 4x-1 = 0, y -x -3 = 0 and x +y -5 = 0 .

The sides of a triangle are 3x+4y, 4x +3y and 5x +5y where, x, y gt 0, then the triangle is-

If the lines y = 3x + 1 " and " 2y = x + 3 are equally inclined to the line y = mx + 4 ,find the value of m.

The number of integral values of m for which the x-coordinate of the point of intersection of the lines 3x+4y=9 and y=m x+1 is also an integer is 2 (b) 0 (c) 4 (d) 1

The locus of centroid of triangle formed by a tangent to the parabola y^(2) = 36x with coordinate axes is (a) y^(2) =- 9x (b) y^(2) +3x = 0 (c) y^(2) = 3x (d) y^(2) = 9x

CENGAGE PUBLICATION-STRAIGHT LINES-EXERCISE (SINGLE CORRECT ANSWER TYPE)
  1. If the extremities of the base of an isosceles triangle are the points...

    Text Solution

    |

  2. A-=(-4,0),B-=(4,0)dotMa n dN are the variable points of the y-axis s...

    Text Solution

    |

  3. The number of triangles that the four lines y = x + 3, y = 2x + 3, y =...

    Text Solution

    |

  4. A variable line x/a + y/b = 1 moves in such a way that the harmonic me...

    Text Solution

    |

  5. Given A (0, 0) and B (x,y)with x epsilon (0,1) and y>0. Let the slope ...

    Text Solution

    |

  6. A triangle is formed by the lines x+y=0,x-y=0, and l x+m y=1. If la n ...

    Text Solution

    |

  7. Let P be (5, 3) and a point R on y=x and Q on the x-axis be such that ...

    Text Solution

    |

  8. If a pair of perpendicular straight lines drawn through the origin f...

    Text Solution

    |

  9. A point P(x,y) moves that the sum of its distance from the lines 2x-y-...

    Text Solution

    |

  10. If AD, BE and CF are the altitudes of Delta ABC whose vertex A is (-4,...

    Text Solution

    |

  11. The vertex A of DeltaABC is (3,-1). The equation of median BE and angl...

    Text Solution

    |

  12. Suppose A, B are two points on 2x-y+3=0 and P(1,2) is such that PA=PB....

    Text Solution

    |

  13. Triangle formed by variable lines (a+b)x+(a-b)y-2ab=0 and (a-b)x+(a+b)...

    Text Solution

    |

  14. A light ray coming along the line 3x+4y=5 gets reflected from the line...

    Text Solution

    |

  15. The point (2,1) , translated parallel to the line x-y=3 by the distanc...

    Text Solution

    |

  16. If one diagonal of square is the portion of the line x/a+y/b=1intercep...

    Text Solution

    |

  17. The point P(2,1) is shifted through a distance 3sqrt(2) units measured...

    Text Solution

    |

  18. Let O be the origin. If A(1,0)a n dB(0,1)a n dP(x , y) are points such...

    Text Solution

    |

  19. In a triangle A B C , the bisectors of angles Ba n dC lies along the l...

    Text Solution

    |

  20. Line a x+b y+p=0 makes angle pi/4 with xcosalpha+ysinalpha=p ,p in R^...

    Text Solution

    |