Q78 / 160 · AP EAMCET 2015 · Mathematics

The point $(2,3)$ is first reflected in the straight line $y=x$ and then translated through a distance of 2 units along the positive direction $X$-axis. The coordinates of the transformed point are

  • A
    $(5,4)$
  • B
    $(2,3)$
  • Correct answer
    C
    $(5,2)$
  • D
    $(4,5)$

Solution

Let $P(2,3)$ be the given point and $Q$ be the reflection of point $P(2,3)$ about the line $y=x$. Then, the coordinates of $Q$ are $(3,2)$ Now, the point $Q$ is translated through a distance of 2 units along the positive direction of $X$-axis. Let the new position of $Q$ be $R$. Then, the coordinates of $R$ are $\begin{aligned} & R=(3+2,2) \\ & R=(5,2) \end{aligned}$

Hence, the correct answer is option: 'C'.

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