Question

in exercises 4 and 5, graph △cde and its image after a reflection in the given line.

1. c(3,4), d(5, - 2), e(0, - 5); y - axis (mark the y - axis with dashed line)
2. c(1,6), d(2,2), e(6,4); y = - 1 (mark the line y = - 1 with dashed line)

Explanation:

Step1: Find the reflection rule

The rule for reflection over the \(y\)-axis is \((x,y)\to(-x,y)\).
For point \(C(3,4)\), its image \(C'\) is \((- 3,4)\) since \(x = 3\) becomes \(-x=-3\) and \(y = 4\) remains the same.
For point \(D(5,-2)\), its image \(D'\) is \((-5,-2)\) as \(x = 5\) changes to \(-x=-5\) and \(y=-2\) is unchanged.
For point \(E(0,-5)\), its image \(E'\) is \((0,-5)\) because \(x = 0\), so \(-x = 0\) and \(y=-5\) stays.

Step2: Plot the points

• Plot the original triangle \(\triangle CDE\) with \(C(3,4)\), \(D(5,-2)\), \(E(0,-5)\).
• Plot the reflected triangle \(\triangle C'D'E'\) with \(C'(-3,4)\), \(D'(-5,-2)\), \(E'(0,-5)\).
• Mark the \(y\)-axis with a dashed line.

Answer:

The coordinates of the image of \(\triangle CDE\) after reflection over the \(y\)-axis are \(C'(-3,4)\), \(D'(-5,-2)\), \(E'(0,-5)\). Plot these points along with the original points and the dashed \(y\)-axis.