10th Class Mathematics Coordinate Geometry Question Bank

done Assertion And Reason (MCQs) - Coordinate Geometry Total Questions - 10

• question_answer1)

  Directions (Q. Nos. 1 - 10): In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:

  Assertion (A): The distance of the point \[P(6,-6)\] from the origin is 6 units.

  Reason (R): The distance between two points \[A({{x}_{1}},{{y}_{1}})\]and \[B({{x}_{2}},{{y}_{2}})\]is given by \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer2)

  Assertion (A): The distance of the point \[(2,11)\] from the X-axis is 11 units.

  Reason (R): The distance of a point \[(x,y)\] from X-axis is its ordinate, i.e., y units.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer3)

  Assertion (A): The distance between the points \[(\sin \theta ,-\cos \theta )\]is 2 units.

  Reason (R): The distance between two points \[A({{x}_{1}},{{y}_{1}})\]and \[B({{x}_{2}},{{y}_{2}})\] is given by \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer4)

  Assertion (A): The point \[P(-4,6)\] divides the join of \[A(-6,10)\]and \[B(3,-8)\] in the ratio \[2:7\].

  Reason (R): If the point \[C(x,y)\] divides the join of \[A({{x}_{1}},{{y}_{1}})\] and \[B({{x}_{2}},{{y}_{2}})\]in the ratio \[m:n,\]then

  \[x=\frac{m{{x}_{2}}+n{{x}_{1}}}{m+n}\] and \[y=\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n}\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer5)

  Assertion (A): The coordinates of the points which divide the line segment joining \[A(2,-8)\] and \[B(-3,-7)\] into three equal parts are \[\left( \frac{1}{3},-\frac{23}{3} \right)\]and \[\left( -\frac{4}{3},-\frac{22}{3} \right)\].

  Reason (R): The points which divide AB in the ratio \[1:3\]and \[3:1\]are called points of trisection of AB.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer6)

  Assertion (A): The coordinates of the centroid of a triangle whose vertices are \[(0,6),\] \[(8,12)\]  and \[(8,0)\] are \[\left( \frac{17}{3},5 \right)\].

  Reason (R): Coordinates of the centroid of a triangle whose vertices are \[({{x}_{1}},{{y}_{1}}),\]\[({{x}_{2}},{{y}_{2}})\] and \[({{x}_{3}},{{y}_{3}})\] are \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\].

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer7)

  Assertion (A): The point \[(0,4)\] lies on Y-axis.

  Reason (R): The x coordinate of the point on Y-axis is zero.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer8)

  Assertion (A): The value of y is 6, for which the distance between the points \[P(2,-3)\] and \[Q(10,y)\] is 10.

  Reason (R): Distance between two given points \[A({{x}_{1}},{{y}_{1}})\]and \[B({{x}_{2}},{{y}_{2}})\] is given 6.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer9)

  Assertion (A): Mid-point of a Line segment divides line in the ratio \[1:1\]

  Reason (R): If area of triangle is zero that means points are collinear.

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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• question_answer10)

  Assertion (A): Centroid of a triangle formed by the points \[(a,b),\]\[(b,c)\]  and \[(c,a)\] is at origin. Then \[\text{a}+\text{b}+c=0.\].

  Reason (R): Centroid of a \[\Delta ABC\] with vertices \[A({{x}_{1}},{{y}_{1}}),\] \[B({{x}_{2}},{{y}_{2}})\]and \[C({{x}_{3}},{{y}_{3}})\] is given by \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\,\,\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\]

  A)
  Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) done clear
  B)
  Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A). done clear
  C)
  Assertion (A) is true but reason (R) is false. done clear
  D)
  Assertion (A) is false but reason (R) is true. done clear
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