Question

directions: graph and label each figure and its image under the given transformation.
give the new coordinates.
7 square tuvw with vertices t(-6, 1), u(-1, 0), v(-2, -5), and w(-7, -4):
(a) reflection: in the y-axis
(b) translation: (x, y)→(x - 5, y + 7)

1. triangle fgh with vertices f(6, 6), g(8, 8),

and h(8, 3):
(a) reflection: in the line x = 5
(b) translation: (x, y)→(x - 7, y - 9)

1. triangle lmn with vertices l(-7, 4), m(-3, 0),

and n(-8, 1):
(a) translation: (x, y)→(x + 5, y - 6)
(b) reflection: in the line y = -x

1. rectangle abcd with vertices a(1, 0),

b(7, 2), c(8, -1), and d(2, -3):
(a) translation: (x, y)→(x - 8, y - 3)
(b) reflection: in the x-axis

Explanation:

Step1: Reflection in the y - axis

For a point \((x,y)\) reflected over the \(y\) - axis, the transformation rule is \((x,y)\to(-x,y)\).

• For \(T(-6,1)\): \((-6,1)\to T'(6,1)\)
• For \(U(-1,0)\): \((-1,0)\to U'(1,0)\)
• For \(V(-2,-5)\): \((-2,-5)\to V'(2,-5)\)
• For \(W(-7,-4)\): \((-7,-4)\to W'(7,-4)\)

Step2: Translation \((x,y)\to(x - 5,y + 7)\)

• For \(T(-6,1)\): \(x=-6,y = 1\), \(x-5=-6 - 5=-11\), \(y + 7=1+7 = 8\), so \(T'(-11,8)\)
• For \(U(-1,0)\): \(x=-1,y = 0\), \(x-5=-1-5=-6\), \(y + 7=0 + 7=7\), so \(U'(-6,7)\)
• For \(V(-2,-5)\): \(x=-2,y=-5\), \(x-5=-2-5=-7\), \(y + 7=-5 + 7=2\), so \(V'(-7,2)\)
• For \(W(-7,-4)\): \(x=-7,y=-4\), \(x-5=-7-5=-12\), \(y + 7=-4 + 7=3\), so \(W'(-12,3)\)

Answer:

\(T'(6,1)\), \(U'(1,0)\), \(V'(2,-5)\), \(W'(7,-4)\) (for reflection in \(y\) - axis)
\(T'(-11,8)\), \(U'(-6,7)\), \(V'(-7,2)\), \(W'(-12,3)\) (for translation \((x,y)\to(x - 5,y + 7)\))