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 \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] |
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. |
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 \[AB=\sqrt{{{({{x}_{2}}-{{x}_{1}})}^{2}}+{{({{y}_{2}}-{{y}_{1}})}^{2}}}\] |
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 \[y=\frac{m{{y}_{2}}+n{{y}_{1}}}{m+n}\] |
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. |
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 \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\]. |
Assertion (A): The point \[(0,4)\] lies on Y-axis. |
Reason (R): The x coordinate of the point on Y-axis is zero. |
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. |
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. |
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 \[\left( \frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}}{3},\,\,\frac{{{y}_{1}}+{{y}_{2}}+{{y}_{3}}}{3} \right)\] |
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