b. Find the image of a point \( A(3,4) \) after reflection in \( x \)-axis. 5.a. What is the formula of mean deviation from median in discrete series. Group- \( B[8 \times 2=16] \) b. Define transpose matrix of \( A \). 6.a. Define Rectangular matrix with example. b. If \( A=\left[\begin{array}{ll}1 & 3 \\ 2 & 4\end{array}\right] \) and \( B=\left[\begin{array}{ll}3 & 2 \\ 6 & 4\end{array}\right] \) then find \( A B \). 7.a. Find the distance between the points \( A(-2,1) \) and \( B(4,3) \). b. For what value of \( K \) will be the point \( (2,1) \) lie on the curve. \( k x^{2}-2 y^{2}-2 x+3 y-3=0 \) ? 8.a. Find the mid - point of the line joining the points \( (-3,6) \) and \( (1,-2) \) b. Prove that: \( \left(1-\cos ^{2} \theta\right) \). \( \left(1+\cot ^{2} \theta\right)=1 \) 9.a. If \( A(1,3) \) and \( B(6,3) \) are the two end points of \( \overrightarrow{A B} \). Find \( \overrightarrow{A B} \) and hence find \( |\overrightarrow{A B}| \).
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Bonus Knowledge
To find the image of point \( A(3,4) \) after reflection in the \( x \)-axis, you simply need to change the sign of the \( y \)-coordinate. So, the reflected point will be \( A'(3, -4) \). It's like taking a selfie—just flipping it upside down! The mean deviation from the median in a discrete series is calculated using the formula: \[ \text{MD} = \frac{\sum |x_i - M|}{N} \] where \( x_i \) represents each data point, \( M \) is the median, and \( N \) is the number of data points. Just think of it as measuring how far each number is from the central trend (the median) and averaging those distances!
