Question

directions: graph and label each figure and its image under the given reflection. give the new coordinates.

1. square bcde with vertices b(-6, 7), c(-2, 6), d(-3, 2), and e(-7, 3) in the y - axis.
2. triangle fgh with vertices f(1, 8), g(5, 7), and h(2, 3) in the line y = x.
3. trapezoid jklm with vertices j(-4, 3), k(-2, 7), l(2, 7), and m(3, 3) in the line y = 1.
4. rhombus wxyz with vertices w(1, 5), x(6, 3), y(1, 1), and z(-4, 3) in the x - axis.
5. triangle pqr with vertices p(-2, 3), q(2, 4), and r(1, -1) in the line x = -3.
6. rectangle mnop with vertices m(-7, 1), n(-4, 1), o(-4, -4), and p(-7, -4) in the line y = -x.

Explanation:

Step1: Reflection rule for y - axis

The rule for reflecting a point $(x,y)$ over the y - axis is $(-x,y)$.
For square $BCDE$:
For $B(-6,7)$, $B'=(6,7)$;
For $C(-2,6)$, $C'=(2,6)$;
For $D(-3,2)$, $D'=(3,2)$;
For $E(-7,3)$, $E'=(7,3)$.

Step2: Reflection rule for line $y = x$

The rule for reflecting a point $(x,y)$ over the line $y = x$ is $(y,x)$.
For triangle $FGH$:
For $F(1,8)$, $F'=(8,1)$;
For $G(5,7)$, $G'=(7,5)$;
For $H(2,3)$, $H'=(3,2)$.

Step3: Reflection rule for line $y = 1$

The distance between a point $(x,y)$ and the line $y = 1$ is $d=\vert y - 1\vert$. The new y - coordinate is $1-(y - 1)=2 - y$ (when $y>1$) or $1+(1 - y)=2 - y$ (when $y<1$).
For trapezoid $JKLM$:
For $J(-4,3)$, $J'(-4,-1)$;
For $K(-2,7)$, $K'(-2,-5)$;
For $L(2,7)$, $L'(2,-5)$;
For $M(3,3)$, $M'(3,-1)$.

Step4: Reflection rule for x - axis

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,-y)$.
For rhombus $WXYZ$:
For $W(1,5)$, $W'(1,-5)$;
For $X(6,3)$, $X'(6,-3)$;
For $Y(1,1)$, $Y'(1,-1)$;
For $Z(-4,3)$, $Z'(-4,-3)$.

Step5: Reflection rule for line $x=-3$

The distance between a point $(x,y)$ and the line $x = - 3$ is $d=\vert x+3\vert$. The new x - coordinate is $-3-(x + 3)=-6 - x$.
For triangle $PQR$:
For $P(-2,3)$, $P'(-4,3)$;
For $Q(2,4)$, $Q'(-8,4)$;
For $R(1,-1)$, $R'(-7,-1)$.

Step6: Reflection rule for line $y=-x$

The rule for reflecting a point $(x,y)$ over the line $y=-x$ is $(-y,-x)$.
For rectangle $MNOP$:
For $M(-7,1)$, $M'(-1,7)$;
For $N(-4,1)$, $N'(-1,4)$;
For $O(-4,-4)$, $O'(4,4)$;
For $P(-7,-4)$, $P'(4,7)$.

Answer:

1. $B'(6,7)$, $C'(2,6)$, $D'(3,2)$, $E'(7,3)$
2. $F'(8,1)$, $G'(7,5)$, $H'(3,2)$
3. $J'(-4,-1)$, $K'(-2,-5)$, $L'(2,-5)$, $M'(3,-1)$
4. $W'(1,-5)$, $X'(6,-3)$, $Y'(1,-1)$, $Z'(-4,-3)$
5. $P'(-4,3)$, $Q'(-8,4)$, $R'(-7,-1)$
6. $M'(-1,7)$, $N'(-1,4)$, $O'(4,4)$, $P'(4,7)$