Exercise 4

Chapter 3, Section 3-1, Page 108
enVision Geometry 1st Edition by Al Cuoco
ISBN: 9780328931583

Solution

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Step 1
1 of 5

To find what reflection rule maps triangle to its image, we must clearly define the line of reflection\textbf{define the line of reflection}.

Be certain that the line of reflection is perpendicular bisector of segments between preimage and image points.\textbf{perpendicular bisector of segments between preimage and image points.}

a.\boxed{\quad \text{\textbf{a.}}\quad}

Step 1:\textbf{Step 1:}

Write the coordinates of preimage and image:

C(3,8)D(5,12)E(4,6)C(3,8) \quad D(5,12) \quad E(4,6)

C(8,3)D(12,5)E(6,4)C'(-8,-3) \quad D'(-12,-5) \quad E'(-6,-4)

Step 2:\textbf{Step 2:}

Find the midpoints of the segment connecting two pairs of corresponding points.

Midpoint of CC\overline{CC'}:

(3+(8)2,8+(3)2)=(52,52)=(2.5,2.5)\left( \frac{3+(-8)}{2},\frac{8+(-3)}{2}\right)=\left( \frac{-5}{2},\frac{5}{2}\right)=(-2.5,2.5)

Midpoint of EE\overline{EE'}:

(4+(6)2,6+(4)2)=(22,22)=(1,1)\left( \frac{4+(-6)}{2},\frac{6+(-4)}{2}\right)=\left( \frac{-2}{2},\frac{2}{2}\right)=(-1,1)

(Remember that the line is uniquely determined by two points.Therefore, only 2 midpoints is sufficient to calculate.)\textit{(Remember that the line is uniquely determined by two points.\\ Therefore, only 2 midpoints is sufficient to calculate.)}

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