Question

reflect the figure over the line $x = 1$.
plot all of the points of the reflected figure.
you may click a plotted point to delete it.
answer attempt 1 out of 6

Explanation:

Step1: Find the distance between each point and the line \(x = 1\)

Let's assume the original points are \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\). The distance of a point \((x,y)\) from the line \(x = 1\) is \(d=\vert x - 1\vert\).

Step2: Calculate the \(x\) - coordinate of the reflected points

The formula for reflecting a point \((x,y)\) over the line \(x = a\) is \((2a - x,y)\). Here \(a = 1\), so the reflected point of \((x,y)\) is \((2\times1 - x,y)=(2 - x,y)\)
Suppose the original points are \((3,-1)\), \((6,-2)\), \((4,-8)\)
For the point \((3,-1)\):
The reflected \(x\) - coordinate is \(2\times1-3=-1\), and the \(y\) - coordinate remains \(-1\). So the reflected point is \((-1,-1)\)
For the point \((6,-2)\):
The reflected \(x\) - coordinate is \(2\times1 - 6=-4\), and the \(y\) - coordinate remains \(-2\). So the reflected point is \((-4,-2)\)
For the point \((4,-8)\):
The reflected \(x\) - coordinate is \(2\times1-4=-2\), and the \(y\) - coordinate remains \(-8\). So the reflected point is \((-2,-8)\)

Answer:

The reflected points are \((-1,-1)\), \((-4,-2)\), \((-2,-8)\)