the rectangle ( ijkl ) is a dilation of the rectangle ( ijkl ). what is the scale factor of the…

the rectangle ( ijkl ) is a dilation of the rectangle ( ijkl ). what is the scale factor of the dilation?\nsimplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

the rectangle ( ijkl ) is a dilation of the rectangle ( ijkl ). what is the scale factor of the dilation?\nsimplify your answer and write it as a proper fraction, an improper fraction, or a whole number.

Answer

Explanation:

Step1: Find the length of a side of the original rectangle

The length of (KL) (original rectangle (IJKL)): (K(8,10)), (L(8,2)). Using the distance formula for vertical points (since (x -)coordinates are the same), (d=\vert y_2 - y_1\vert). So (KL=\vert10 - 2\vert=8).

Step2: Find the length of the corresponding side of the dilated rectangle

The length of (K'L') (dilated rectangle (I'J'K'L')): (K'(4,5)), (L'(4,1)). Using the distance formula for vertical points (since (x -)coordinates are the same), (d=\vert y_2 - y_1\vert). So (K'L'=\vert5 - 1\vert = 4).

Step3: Calculate the scale factor

The scale factor (s) of a dilation is given by (s=\frac{\text{length of side of dilated figure}}{\text{length of side of original figure}}). So (s=\frac{K'L'}{KL}=\frac{4}{8}=\frac{1}{2}).

Answer:

(\frac{1}{2})