Equation of line in Straight lines

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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

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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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Equation of line in Straight lines

Remember concepts with our Masterclasses.

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

Suppose that the midpoint of the line segment joining the points 1,2 and 3,4 is PHence, P=x1+x22,y1+y22=1+32,2+42=2,3 The image of the point Px1,y1 in the line y=x is y1,x1Therefore, the image of the point P2,3 in the line y=x is a,b=3,2It implies that a+b=3+2=5

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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