First slide

Equation of line in Straight lines

Question

Reflection of the midpoint of the line segment joining the points $(1, 2)$ and $(3, 4)$ with respect to the line $y = x$ is $(a, b)$ . The value of $a + b$ is

Moderate

A

2
B

3
C

4
D

5

Solution

$Suppose that the midpoint of the line segment joining the points (1, 2) and (3, 4) is P$
Hence,
$\begin{matrix} P = (\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\ = (\frac{1 + 3}{2}, \frac{2 + 4}{2}) \\ = (2, 3) \end{matrix}$
$The image of the point P (x_{1}, y_{1}) in the line y = x is (y_{1}, x_{1})$
$Therefore, the image of the point P (2, 3) in the line y = x is (a, b) = (3, 2)$
$It implies that a + b = 3 + 2 = 5$

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