Question

3.2 assignment
2 of 5
what are the coordinates of the image after the reflection in the given line.
x = - 1

Explanation:

Step1: Recall reflection rule

For a reflection over the line $x = a$, the formula for reflecting a point $(x,y)$ is $(2a - x,y)$. Here $a=- 1$.

Step2: Assume coordinates of points

Let's assume point $A=(x_A,y_A)$, $B=(x_B,y_B)$, $C=(x_C,y_C)$. After reflection over $x = - 1$, the new - coordinates are $A'=(2\times(-1)-x_A,y_A)=(-2 - x_A,y_A)$, $B'=(-2 - x_B,y_B)$, $C'=(-2 - x_C,y_C)$. But since we don't have the original coordinates of $A$, $B$ and $C$ from the image clearly, we'll use a general approach. If a point $(x,y)$ is reflected over $x=-1$, the distance between the point and the line $x = - 1$ is calculated in the $x$ - direction. The new $x$ - coordinate of the reflected point is found by moving the same distance on the other side of the line $x=-1$.

Step3: Calculate for a sample point

Suppose a point $P=(x,y)$. The distance from $P$ to the line $x=-1$ is $d=\vert x+1\vert$. The new $x$ - coordinate $x'=-1 - d$ if $x\geq - 1$ and $x'=-1 + d$ if $x\lt - 1$. In general, $x'=-2 - x$. The $y$ - coordinate remains the same.

Answer:

Without the original coordinates of $A$, $B$ and $C$, we can only say that if $A=(x_1,y_1)$, $A'=(-2 - x_1,y_1)$; if $B=(x_2,y_2)$, $B'=(-2 - x_2,y_2)$; if $C=(x_3,y_3)$, $C'=(-2 - x_3,y_3)$