the trapezoid ( klmn ) is a dilation of the trapezoid ( klmn ). what is the scale factor of the…

Explanation:

Step1: Find the length of a corresponding side in both trapezoids

Let's take the side (KL). The coordinates of (K=(1,6)) and (L=(1,4)). Using the distance formula (d = |y_2 - y_1|) (since (x)-coordinates are the same), (KL=|6 - 4| = 2). For the side (K'L'), the coordinates of (K'=(0,4)) and (L'=(0,2)). Using the distance formula (d = |y_2 - y_1|) (since (x)-coordinates are the same), (K'L'=|4 - 2| = 2). Wait, no, let's take another pair. Let's take (KN). (K=(1,6)), (N=(-1,-6)). Using the distance formula (d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}), (d_{KN}=\sqrt{( - 1-1)^2+(-6 - 6)^2}=\sqrt{(-2)^2+(-12)^2}=\sqrt{4 + 144}=\sqrt{148}). (K'=(0,4)), (N'=(-1,-2)). (d_{K'N'}=\sqrt{(-1-0)^2+(-2 - 4)^2}=\sqrt{1+36}=\sqrt{37}). Another approach: Since dilation is a similarity transformation. If we consider the vertical side (KL) (length (2)) and (K'L') (length (2)) was wrong. Let's use the ratio of coordinates. If we assume the center of dilation is the origin (by observation of the graph - lines connecting (K) to (K'), (L) to (L') etc. pass through the origin). For point (K=(1,6)) and (K'=(0.5,3)) (by looking at the graph, more accurately, if we use the formula for dilation ((x,y)\to(kx,ky)). Take (K=(1,6)) and (K'=(0.5,3)). Then (k=\frac{0.5}{1}=\frac{3}{6}=\frac{1}{2})

Step2: Calculate the scale factor

The scale factor (k) of a dilation ((x,y)\to(kx,ky)). Let's use another pair. Take (L=(1,4)) and (L'=(0.5,2)). Using the formula (k=\frac{x_{L'}}{x_L}=\frac{y_{L'}}{y_L}). (\frac{0.5}{1}=\frac{2}{4}=\frac{1}{2})

Answer:

(\frac{1}{2})