Question

A point$P(h,k)$ is reflected in the$x-axis$ to$P\text{'}(2,-3)$write down the values of $h$ and$k$. $P\text{'}\text{'}$ is the image of $P$, when reflected in the $y-axis$. Write down the coordinates of $P\text{'}\text{'}$. Find the coordinates of $P\text{'}\text{'}\text{'}$, when $P$ is reflected in the origin.

Answer 1

Step 1:Finding the values of $\mathit{h}$and $\mathit{k}$:

The reflection of a point$P(x,y)$ in $x-axis$ is given by$P\text{'}(x,-y)$

The reflection of a point$P(h,k)$ in $x-axis$ is$P\text{'}(2,-3)$.

So, the point $P(h,k)$ is$(2,3)$, where $h=2$and$k=3$.

Step 2: Finding the coordinates of$\mathit{P}\mathbf{\text{'}\text{'}}$.

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

Therefore, the reflection of a point $P(2,3)$ in the$y-axis$ is$P\text{'}\text{'}(-2,3)$.

Step 3: Finding the coordinates of$\mathit{P}\mathbf{\text{'}}\mathbf{\text{'}}\mathbf{\text{'}}$.

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

The reflection of a point $P(2,3)$ in the origin is$P\text{'}\text{'}\text{'}(-2,-3)$.

Hence, the coordinates of the point $P$are $(2,3)$

The coordinates of the image $P\text{'}\text{'}$are $(-2,3)$ and

The coordinates of the image $P\text{'}\text{'}\text{'}$are$(-2,-3)$.