Question

The point$B(1,7)$ on the reflection in the line $y=0$ is mapped on$B\text{'}$. the point $B\text{'}$ on reflection in the origin is mapped on$B\text{'}\text{'}$. find the coordinates of$B\text{'}$ and $B\text{'}\text{'}$. also write down a single transformation that maps $B$ and$B\text{'}\text{'}$.

Answer 1

Step 1: Finding the image of a given point in the line $y=0$

The line $y=0$ is nothing but the $x-axis$

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

Thus, the reflection of a point $B(1,7)$ in the line$y=0$ is the point$B\text{'}(1,-7)$

Step 2: Finding the Reflection of $B\text{'}$in the origin.

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

Thus, the reflection of a point $B\text{'}(1,-7)$ in the origin will be$B\text{'}\text{'}$$(-1,7)$.

Step 3: Single transformation that maps $B$ and$B\text{'}\text{'}$.

The single transformation that maps$B(1,7)$ to the point$B\text{'}\text{'}(-1,7)$ is simply the reflection in $y-axis$ as only the sign of abscissa$\left(1\right)$ is changing and the sign ordinate $\left(7\right)$ remains the same.

Therefore, the coordinates of the image $B\text{'}$is $(1,-7)$

The coordinate of the image $B\text{'}\text{'}$is $(-1,7)$

The single transformation that maps$B(1,7)$ to the point $B\text{'}\text{'}(-1,7)$ is the reflection in$y-axis$.