Question

question 5 4-1 homework describe the transformation. use decimals, if necessary. reflection in the line y =

Explanation:

Step1: Find mid - points of corresponding points

For a reflection, the line of reflection is the perpendicular bisector of the line segment joining a point and its image. Let's take a point, say \(M(1,4)\) and its image \(M'(1, - 8)\). The mid - point of the line segment \(MM'\) is calculated using the mid - point formula \((\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Here \(x_1=1,x_2 = 1,y_1 = 4,y_2=-8\), so the mid - point is \((\frac{1 + 1}{2},\frac{4+( - 8)}{2})=(1,-2)\).

Step2: Determine the line of reflection

Since the \(x\) - coordinates of corresponding points (e.g., \(M\) and \(M'\), \(N\) and \(N'\), \(L\) and \(L'\), \(K\) and \(K'\)) are the same, the line of reflection is a horizontal line. The \(y\) - coordinate of the mid - points of all corresponding points is \(y=-2\). So the figure is reflected in the line \(y=-2\).

Answer:

\(-2\)