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Coordinate Geometry Test - 33

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Coordinate Geometry Test - 33
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  • Question 1
    1 / -0
    An abscissa of a point $$P$$ is negative and ordinate of $$P$$ is positive, then $$P$$ lies in:
    Solution
    The abscissa of a point means the $$x$$ - coordinate of the point.
    The ordinate of a point means the $$y$$ - coordinate of the point. 
    If both coordinates are positive, the point must be located in quadrant $$1$$. 
    If only one coordinate is positive, the point is either in quadrant $$2$$ or quadrant $$4$$.
    If only the first coordinate is positive, then the point is in quadrant $$4$$. 
    If only the second coordinate is positive, then the point is in quadrant $$2$$.
    Here, the first coordinate is negative and the second coordinate is positive, then the point is in quadrant $$2$$. 
  • Question 2
    1 / -0
    Which of the following points lies in second quadrant?
    Solution

  • Question 3
    1 / -0
    In which of the following quadrants does the point $$ P (2 , -3) $$  lie ? 
    Solution
    We know that, abscissa and coordinates in
    First quadrant   $$X=$$ positive   and  $$Y=$$ positive
    Second quadrant  $$X=$$ negative   and  $$Y=$$ positive
    Third quadrant   $$X=$$ negative   and  $$Y=$$ negative
    Fourth quadrant  $$X=$$ positive   and  $$Y= $$ negative
    $$(2,-3)$$ has $$X=2,$$ positive and $$Y=-3$$, negative
    Therefore point $$P(2,-3)$$ lies in $$IV$$ quadrant.
  • Question 4
    1 / -0
    In which of the following quadrants does the point $$ P (-7, -1) $$  lie ? 
    Solution
    Values of abscissa and ordinate are different in all three quadrants.

    First quadrant   $$X=$$ positive   and  $$Y=$$ positive

    Second quadrant  $$X=$$ negative   and  $$Y=$$ positive

    Third quadrant   $$X=$$ negative   and  $$Y=$$ negative

    Fourth quadrant  $$X=$$ positive   and  $$Y= $$ negative

    $$(-7,-1)$$ has $$X=-7,$$ which is negative   and $$Y=-1$$ which is also negative   

    Therefore point $$P(-7,-1)$$ lies in quadrant $$III$$
  • Question 5
    1 / -0
    In which of the following quadrant does the point $$ P(3 , 6) $$ lie ? 
    Solution
    We know that, abscissa and coordinates in
    First quadrant   $$X=$$ positive   and  $$Y=$$ positive
    Second quadrant  $$X=$$ negative   and  $$Y=$$ positive
    Third quadrant   $$X=$$ negative   and  $$Y=$$ negative
    Fourth quadrant  $$X=$$ positive   and  $$Y= $$ negative
    $$(3,6)$$ has $$X=3,$$ positive and $$Y=6$$, positive 
    Therefore point $$P(3,6)$$ lies in $$I$$ quadrant.
  • Question 6
    1 / -0
    On plotting the points $$O \left(0,0\right) , A \left(3,0\right), B \left(3,4\right) , C \left(0,4\right)$$ and joining OA, AB, BC and CO which of the following figure is obtained ?
  • Question 7
    1 / -0
    The points $$\left(-5,2\right)$$ and $$\left(2,-5\right)$$ lie in the 
    Solution
    In point $$\left(-5,2\right)$$, $$x$$ - coordinate is negative and $$y$$ - coordinate is positive, so it lies in $$II$$ quadrant and in the point $$\left(2,-5\right)$$, $$x$$ - coordinate is positive and  $$y$$ - coordinate is negative, so it lies in $$IV$$ quadrant.
    Hence, $$\left(C\right)$$ is the correct answer.
  • Question 8
    1 / -0
    Signs of the abscissa and ordinate of a point in the second quadrant are respectively: 
    Solution
    $$\textbf{Step 1: Checking the value of abscissa and ordinate in the second quadrant}$$

                    $$\text{The second quadrant consists of the negative x-axis and positive y axis}$$

                    $$\therefore\text{ Abscissa is negative and Ordinate is positive}$$

    $$\textbf{Hence, the sign of abscissa and ordinate in the second quadrant is (-,+)}$$
  • Question 9
    1 / -0
    Points $$\left(1,-1\right), \left(2,-2\right), \left(4, -5\right), \left(-3,-4\right)$$
    Solution
    In points $$\left(1,-1\right), \left(2,-2\right)$$ and $$\left(4,-5\right)$$ x - coordinate is positive and y - coordinate is negative. So, they all lie in $$IV$$ quadrant. In point $$\left(-3,-4\right)$$ x - coordinate is negative and y - coordinate is negative. So, it lies in $$III$$ quadrant. So, given points do not lie in the same quadrant.
    Hence, $$\left(D\right) $$ is the correct answer.
  • Question 10
    1 / -0
    The points whose abscissa and ordinate have different signs will lie in 
    Solution
    The points whose abscissa and ordinate have different sings will be of the from $$\left(-x, y\right)$$ or $$\left(x, -y\right)$$ and these points will lie in $$II$$ and $$IV$$ quadrants.
     Hence, $$\left(D\right)$$ is the correct answer.
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