Question

example 2:
given \\( \triangle lmn \\) with vertices \\( l(4,8), m(0,8) \\) and \\( n(0,2) \\). draw and list the coordinates.
a. reflect over the \\( x \\)-axis.
b. translate 2 units right and 4 units up.
c. rotate \\( 90^{\circ} \\) counterclockwise about the origin.
a. \\( l \\)________ \\( m \\)______ \\( n \\)________
b. \\( l \\)________ \\( m \\)______ \\( n \\)________
c. \\( l \\)________ \\( m \\)______ \\( n \\)________
example 3:
given quadrilateral defg with vertices \\( d(1,2), e(3,1) \\), \\( f(5,1) \\), and \\( g(5,3) \\).
a. translate 5 units left, and 3 units down.
b. reflect across the \\( y \\)-axis.
c. rotate \\( 180^{0} \\) about the origin
a. \\( d \\)________ \\( e \\)______ \\( f \\)______ \\( g \\)________
b. \\( d \\)________ \\( e \\)______ \\( f \\)______ \\( g \\)________
c. \\( d \\)________ \\( e \\)______ \\( f \\)______ \\( g \\)________

Explanation:

Example 2:

Part a: Reflection over the x - axis

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

• For \(L(4,8)\): \(L'(4,-8)\)
• For \(M(0,8)\): \(M'(0,-8)\)
• For \(N(0,2)\): \(N'(0,-2)\)

Part b: Translation 2 units right and 4 units up

The translation rule is \((x,y)\to(x + 2,y+4)\).

• For \(L'(4,-8)\): \(L''(4 + 2,-8 + 4)=(6,-4)\)
• For \(M'(0,-8)\): \(M''(0+2,-8 + 4)=(2,-4)\)
• For \(N'(0,-2)\): \(N''(0 + 2,-2+4)=(2,2)\)

Part c: Rotation \(90^{\circ}\) counter - clockwise about the origin

The rotation rule for a \(90^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(-y,x)\).

• For \(L''(6,-4)\): \(L'''(4,6)\)
• For \(M''(2,-4)\): \(M'''(4,2)\)
• For \(N''(2,2)\): \(N'''(-2,2)\)

Example 3:

Part a: Translation 5 units left and 3 units down

The translation rule is \((x,y)\to(x-5,y - 3)\).

• For \(D(1,2)\): \(D'=(1-5,2 - 3)=(-4,-1)\)
• For \(E(3,1)\): \(E'=(3-5,1 - 3)=(-2,-2)\)
• For \(F(5,1)\): \(F'=(5-5,1 - 3)=(0,-2)\)
• For \(G(5,3)\): \(G'=(5-5,3 - 3)=(0,0)\)

Part b: Reflection across the y - axis

The reflection rule is \((x,y)\to(-x,y)\).

• For \(D'(-4,-1)\): \(D''=(4,-1)\)
• For \(E'(-2,-2)\): \(E''=(2,-2)\)
• For \(F'(0,-2)\): \(F''=(0,-2)\)
• For \(G'(0,0)\): \(G''=(0,0)\)

Part c: Rotation \(180^{\circ}\) about the origin

The rotation rule is \((x,y)\to(-x,-y)\).

• For \(D''(4,-1)\): \(D'''=(-4,1)\)
• For \(E''(2,-2)\): \(E'''=(-2,2)\)
• For \(F''(0,-2)\): \(F'''=(0,2)\)
• For \(G''(0,0)\): \(G'''=(0,0)\)

Answer:

Example 2:

a. \(L'(4,-8)\), \(M'(0,-8)\), \(N'(0,-2)\)
b. \(L''(6,-4)\), \(M''(2,-4)\), \(N''(2,2)\)
c. \(L'''(4,6)\), \(M'''(4,2)\), \(N'''(-2,2)\)

Example 3:

a. \(D'(-4,-1)\), \(E'(-2,-2)\), \(F'(0,-2)\), \(G'(0,0)\)
b. \(D''(4,-1)\), \(E''(2,-2)\), \(F''(0,-2)\), \(G''(0,0)\)
c. \(D'''(-4,1)\), \(E'''(-2,2)\), \(F'''(0,2)\), \(G'''(0,0)\)