Question

A point $P$ is reflected in the $x=0$ and the coordinates of its image are$(-1,2).$

$i.$Find the coordinates of$P$

$ii.$Find the coordinates of the image $P$ under the reflection in the line$y=0$

$iii.$Find the coordinates of the image $P$under the reflection in the origin.

Answer 1

Step 1: Finding the coordinates of the point$P$

The line $x=0$ is nothing but$y-axis$ and the reflection of a point $(x,y)$ in $y-axis$ is given by $(-x,y).$

The reflection of the point $P$ $(x,y)$in the line $x=0$ is given as $P\text{'}$$(-1,2)$.

Therefore, the coordinates of$P(x,y)$are$(1,2)$, where $x=1$and$y=2$.

Step 2: Finding the image of P in the line $y=0$

The line$y=0$ is nothing but $x-axis$ and the reflection of a point$(x,y)$ in $x-axis$ is given by$(x,-y)$.

Therefore, the reflection of the point$P(1,2)$ in the line $y=0$ is $P\text{'}(1,-2).$

Step 3: Finding the image of$P$ under the reflection in the origin

The reflection of a point$P$$(x,y)$ in the origin is$O(0,0)$ given by$P\text{'}\text{'}$$(-x,-y)$.

Therefore, the reflection of the point $P(1,2)$ in the origin is$P\text{'}\text{'}(-1,-2)$.

Hence, The coordinates of the point $P$ are$(1,2)$,

The image of $P$ in the line $y=0$ is $P\text{'}(-1,2)$ and

The coordinate of the image$P(1,2)$ under the reflection in origin is$P\text{'}\text{'}(-1,-2)$.