Question

reflect the figure over the line y = 1. plot all of the points of the reflected figure. you may click a plotted point to delete it.

Explanation:

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

Let's assume the original points are \((x_1,y_1)\), \((x_2,y_2)\), \((x_3,y_3)\), \((x_4,y_4)\). The distance \(d\) from a point \((x,y)\) to the line \(y = 1\) is \(d=\vert y - 1\vert\).

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

The formula for reflecting a point \((x,y)\) over the line \(y = c\) (here \(c = 1\)) is \((x,2c - y)\). So for a point \((x,y)\), its reflection over \(y = 1\) is \((x,2\times1 - y)=(x,2 - y)\)

Step3: Apply the formula to each vertex of the figure

Suppose the original vertices are \((- 8,9)\), \((-3,8)\), \((-1,6)\), \((-8,3)\)

• For the point \((-8,9)\): Using the formula \((x,2 - y)\), we get \((-8,2-9)=(-8,-7)\)
• For the point \((-3,8)\): Using the formula \((x,2 - y)\), we get \((-3,2 - 8)=(-3,-6)\)
• For the point \((-1,6)\): Using the formula \((x,2 - y)\), we get \((-1,2-6)=(-1,-4)\)
• For the point \((-8,3)\): Using the formula \((x,2 - y)\), we get \((-8,2 - 3)=(-8,-1)\)

Answer:

Plot the points \((-8,-7)\), \((-3,-6)\), \((-1,-4)\), \((-8,-1)\)