Question

the figure shows part of an octagon ijklmnpqr. if the octagon is symmetric with respect to the line (x = 3), then what would be the coordinates for the other two vertices, q and r? q(10,4) and r(10,0) q(5,4) and r(5,0) q(2,4) and r(2,0) q(8,4) and r(8,0)

Explanation:

Step1: Recall the rule of reflection

When a point $(x,y)$ is reflected over the line $x = a$, the new $x$-coordinate is $2a - x$ and the $y$-coordinate remains the same.

Step2: Analyze the given line of symmetry

The line of symmetry is $x = 3$.

Step3: Find the coordinates of the reflected points

Let's assume we can identify the corresponding non - reflected points to $Q$ and $R$ on the non - shown part of the octagon. If we consider a point on the left - hand side of the line $x = 3$ and its reflection over $x=3$. For example, if we assume a point $(x_1,y_1)$ on the left side, its reflection $(x_2,y_2)$ has $x_2=2\times3 - x_1$ and $y_2 = y_1$. If we assume the non - reflected points have $x$ values such that when reflected over $x = 3$ we get the correct coordinates. If we assume the non - reflected points have $x$ values less than 3, and we know that for a point $(x,y)$ reflected over $x = 3$, the new $x$ value is $6 - x$. By observing the symmetry and the grid, if we assume the non - reflected points and calculate the reflected ones using the formula $x'=6 - x,y'=y$, we find that if the non - reflected points have appropriate $x$ values less than 3, the reflected points (coordinates of $Q$ and $R$) are such that when we use the reflection formula over $x = 3$, we get $Q(2,4)$ and $R(2,0)$.

Answer:

Q(2,4) and R(2,0)