First slide

Equation of line in Straight lines

Question

If the lines $x = k; k = 1, 2 \dots, n$ meet the line $y = 3 x + 4$ at the points $A_{k} (x_{k}, y_{k}), k = 1, 2, \dots, n$ then
the ordinate of the centre of Mean position of the points $A_{k}, k = 1, 2, \dots, n$ is

Moderate

A

$\frac{n + 1}{2}$
B

$\frac{3 n + 11}{2}$
C

$\frac{3 (n + 1)}{2}$
D

none of these

Solution

We have $y_{k} = 3 k + 4$ the ordinate of $A_{k}$ , the point of intersection of $x = k$ and $y = 3 x + 4$ . So the ordinate of the centre of Mean position of the points $A_{k}, k = 1, 2, \dots n$ is
$\begin{array}{l} \frac{1}{n} \sum_{k = 1}^{n} y_{k} = \frac{1}{n} \sum_{k = 1}^{n} (3 k + 4) = \frac{3}{n} \sum_{k = 1}^{n} k + 4 \\ = \frac{3 n (n + 1)}{n \cdot 2} + 4 = \frac{3 n + 11}{2} . \end{array}$

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