Question

the polygon shown has a line of reflection that will cause the figure to carry onto itself. complete the equation for the vertical line of reflection (1 point)

Explanation:

Step1: Find midpoint of symmetric x - coordinates

To find the vertical line of reflection, we can take pairs of symmetric points. For example, take the points \((-4,5.8)\) and \((-2,5.8)\). The midpoint formula for the x - coordinate (since it's a vertical line, the y - coordinate doesn't matter for the line equation \(x = a\)) is \(a=\frac{x_1 + x_2}{2}\). Here, \(x_1=-4\) and \(x_2 = - 2\). So \(a=\frac{-4+( - 2)}{2}=\frac{-6}{2}=-3\)? Wait, no, let's check another pair. Take \((-5.4,4.4)\) and \((-0.6,4.4)\). Using the midpoint formula for x - coordinate: \(a=\frac{-5.4+( - 0.6)}{2}=\frac{-6}{2}=-3\)? Wait, no, wait \(-5.4+( - 0.6)=-6\), divided by 2 is - 3? Wait, no, wait \((-5.4,4.4)\) and \((-0.6,4.4)\): the x - coordinates are - 5.4 and - 0.6. The midpoint is \(\frac{-5.4+( - 0.6)}{2}=\frac{-6}{2}=-3\)? Wait, but let's check \((-4,1)\) and \((-2,1)\): midpoint of x - coordinates is \(\frac{-4+( - 2)}{2}=\frac{-6}{2}=-3\). Wait, another pair: \((-5.4,2.4)\) and \((-0.6,2.4)\): midpoint of x - coordinates is \(\frac{-5.4+( - 0.6)}{2}=\frac{-6}{2}=-3\). Wait, so the vertical line of reflection is \(x=-3\)? Wait, no, wait let's recalculate. Wait \(-5.4\) and \(-0.6\): \(-5.4 + 0.6=-4.8\)? No, wait \(-5.4+( - 0.6)=-6\), yes. So \(\frac{-6}{2}=-3\). Wait, but let's check the x - coordinates of the symmetric points. For example, the leftmost x - coordinate related points: \((-5.4,4.4)\) and \((-0.6,4.4)\). The distance between - 5.4 and - 0.6 is \(\vert-5.4-( - 0.6)\vert=\vert-4.8\vert = 4.8\), half of that is 2.4. So - 5.4+2.4=-3, and - 0.6 - 2.4=-3. So the vertical line is \(x = - 3\).

Step2: Confirm with other points

Take the points \((-4,5.8)\) and \((-2,5.8)\). The distance between - 4 and - 2 is 2, half of that is 1. So - 4 + 1=-3, - 2-1=-3. So the vertical line \(x=-3\) is the line of reflection as it is equidistant from the symmetric points.

Answer:

\(x = - 3\)