10 Question MCQ (including Assertion)

In fig 6.52, the area of \(\triangle \mathrm{ABC}\) (in square units) is

If \(P=\left(\frac{a}{3}, 4\right)\) is the mid-point of the line segment joining the points \(Q(-6,5)\) and \(R(-2,3)\), then the value of \(a\) is

The distance of the point \(P(-6,8)\) from the origin is

If the point \(\mathrm{P}(2,1)\) lies on the line segment joining points \(\mathrm{A}(4,2)\) and \(B(8,4)\), then

The perpendicular bisector of the line segment joining the points \(A(1,5)\) and \(B(4,6)\) cuts the \(y\)-axis at

Assertion (A) : The point which divides the line segment joining the points \(A(1,2)\) and \(B(-1,1)\) internally in the ratio \(1: 2\) is \(\left(\frac{-1}{3}, \frac{5}{3}\right)\)

Reason (R) : The coordinates of the point which divides the line segment joining the points \(\mathrm{A}\left(x_1, y_1\right)\) and \(\mathrm{B}\left(x_2, y_2\right)\) in the ratio \(\mathrm{m}_1: \mathrm{m}_2\) are \(\left(\frac{\mathrm{m}_1 x_2+\mathrm{m}_2 x_1}{\mathrm{~m}_1+\mathrm{m}_2}, \frac{\mathrm{~m}_1 \mathrm{y}_2+\mathrm{m}_2 \mathrm{y}_1}{\mathrm{~m}_1+\mathrm{m}_2}\right)\)

If the distance between the points \((2,-2)\) and \((-1, x)\) is 5 , one of the values of \(x\) is

If the diagonals of a quadrilateral divide each other proportionally, then it is a :

The distance between the points \((a \cos \theta+b \sin \theta, 0)\) and \((0, a \sin \theta-b \cos \theta)\) is