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Pair of Straight Lines Test - 4

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Pair of Straight Lines Test - 4
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  • Question 1
    1 / -0

    The image of the point (α,β) with respect to the  line x + y = 0 is

    1. ( - β,−α)

    2. (α,β)

    3. none of these

    4.(β,α)

    Solution

    The equation of the line which is perpendicular to the given line x+y=0 is x - y =0

    The point of intersection of these two lines is (0,0) which is the origin

    This point of intersection is the midpoint of the given point (α,β) and its image, say (a,b)

    Therefore α+a2

    This implies a = −α

    Similarly β+b2 = 0

    This implies b = −β

    Therefore (−α,−β) is the image

  • Question 2
    1 / -0

    Slope of any line parallel to X axis is

    Solution

    Since the angle made with x axis is zero, since tanθ is the slope. Then tan0 = 0

    Hence the slpoe of the line parallel to X-axis is zero

    Option 1 is the correct answer

  • Question 3
    1 / -0
    The vertices of a triangle are (0, 0), (3, 0) and (0, 4). Its orthocentre is at
  • Question 4
    1 / -0

    The image of the point (α,β) with respect to the line x = y is

  • Question 5
    1 / -0
    The equation of the line passing through the points (2, 3) and making an intercept of length 2 units between the lines y + 2x = 3 and y + 2x = 5 is
  • Question 6
    1 / -0

    The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0

    1. 2

    2. none of these

    3. - 2

    4. 8

  • Question 7
    1 / -0
    The incentre of a triangle with vertices (1, ), (0, 0) and (2, 0) is
  • Question 8
    1 / -0
    The straight lines x + y = 0, 3x + y − 4 = 0 and x + 3y − 4 = 0 form which of the following triangles?
  • Question 9
    1 / -0

    Slope of a line is not defined if the line is

    Solution

    Vertical lines hve undefined slopes. Hence a line which is parallel to Y-axis has undefined slopes.

    Hence option 1 is correct.

  • Question 10
    1 / -0
    If P(1, 0), Q(– 1, 0) and R(2, 0) are three given points, then the locus of point S, which satisfies the relation (SQ)2 + (SR)2 = 2(SP)2, is (where SQ, SR and SP are line segments)
  • Question 11
    1 / -0

    The distance of the point ( x , y ) from Y axis is

    1. |x|

    2. y

    3. x

    4. |y|

    Solution

    The abscissa or the x co ordiate of a point  is the distance from the y- axis.

    Hence the distance is x

  • Question 12
    1 / -0
    Orthocentre of the triangle formed by the lines x + y = 1 and xy = 0 is
  • Question 13
    1 / -0
    One of the equations of lines passing through the point (3, − 2) and inclined at 60º to the line x + y = 1 is
  • Question 14
    1 / -0
    If (x, y) are the co-ordinates of a point in the plane, then  = 0 represents
  • Question 15
    1 / -0
    The angle between lines 2x2 − 7xy + 3y2 = 0 is
  • Question 16
    1 / -0
    The orthocenter of the triangle with vertices  and is
  • Question 17
    1 / -0
    The orthocentre of the triangle whose vertices are A (0, 0), B (3, 4) and C (4, 0) is
  • Question 18
    1 / -0

    Projection (the foot of perpendicular) from ( x , y ) on the x – axis is

    Solution

    Let L be the foot of the perpendicular from the X axis. Therefore its y coocrdinate is zero

    Therefore the coordiantes of the point L is (x,0)

    Hence option 1 is the correct answer

  • Question 19
    1 / -0

    The equation y−y1=m(x−x1),m∈R, represents all lines through the point (x1,y1) except the line

    Solution

    The vertical lines which are parallel to Y axis has undefined slopes. Hence the slope of the line 'm' will be undefined.


    Therefore the above equation of the line will represent all lines through (x1,y1) except the line parallel to Y- axis

  • Question 20
    1 / -0
    If the lines x + 2ay + a = 0, x + 3by + b = 0 and x + 4cy + c = 0 are concurrent, then a, b, c are in
  • Question 21
    1 / -0

    The straight lines x + y = 0 , 3x - y – 4 = 0 , x + 3y – 4 = 0 form a triangle which is

    Solution

    The lines formed by these lines is right angled, triangle.


    Two lines are perpendicular to each other if the product  od their slopes is -1


    Slope of the lines  3x - y – 4 = 0 , x + 3y – 4 = 0 are 3 and -1/3 respectively.


    The product of these slopes is -1


    Hence the lines3x - y – 4 = 0 , x + 3y – 4 = 0  are perpendicular to each other.


    Therefore the triangle formed by these lines is a right angled triangle.

  • Question 22
    1 / -0
    The equation of the straight line passing through the intersection of the lines x - 2y = 1 and x + 3y = 2, and parallel to 3x + 4y = 0 is
  • Question 23
    1 / -0
    The distance between the parallel lines given by (x + 7y)2 + 4(x + 7y) − 42 = 0 is
  • Question 24
    1 / -0
    The extremities of diagonal of a parallelogram are the points (3, − 4) and (− 6, 5). If the third vertex is (− 2, 1), then the fourth vertex will be
  • Question 25
    1 / -0

    The distance of the point (α,β) from X axis is

    1. α

    2.|β|

    3.|α|

    4.none of these.

    Solution

    The distance of a  point from X axis is its y coordinate.

    Hence the distance of the point (α,β) from X axis  is |β|

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