Question

period: 2

1. reflect square stuv with s(-4, 4), t(-1, 6), u(1, 3), and v(-2, 1) in the x - axis. what are the coordinates of v?
2. reflect triangle lmn with l(3, 10), m(8, 5), and n(5, 1) in the y - axis. what are the coordinates of m?
3. reflect rhombus abcd with a(-10, 9), b(-6, 7), c(-4, 3), and d(-8, 5) in the y - axis. what are the coordinates of c?
4. translate trapezoid wxyz with w(-1, 1), x(3, 1), y(7, -3) and z(-1, -3) under the rule (x, y)→(x + 2, y + 8). what are the coordinates of z?
5. translate triangle qrs with q(4, 7), r(7, 3) and s(2, -2) under the rule (x, y)→(x - 7, y - 6). what are the coordinates of q?

Explanation:

Step1: Recall reflection rule for x - axis

When reflecting a point $(x,y)$ over the x - axis, the rule is $(x,y)\to(x, - y)$. The point $V(-2,1)$ is reflected over the x - axis.
$V'=(-2,-1)$

Step2: Recall reflection rule for y - axis

When reflecting a point $(x,y)$ over the y - axis, the rule is $(x,y)\to(-x,y)$. For point $M(8,5)$ reflected over the y - axis,
$M'=(-8,5)$

Step3: Apply y - axis reflection rule

For point $C(-4,3)$ reflected over the y - axis using the rule $(x,y)\to(-x,y)$,
$C'=(4,3)$

Step4: Apply translation rule

The translation rule is $(x,y)\to(x + 2,y + 8)$. For point $Z(-1,-3)$, we have $x=-1$ and $y = - 3$.
$x'=-1+2=1$
$y'=-3 + 8=5$
$Z'=(1,5)$

Step5: Apply translation rule

The translation rule is $(x,y)\to(x - 7,y - 6)$. For point $Q(4,7)$, we have $x = 4$ and $y=7$.
$x'=4-7=-3$
$y'=7-6 = 1$
$Q'=(-3,1)$

Answer:

1. $(-2,-1)$
2. $(-8,5)$
3. $(4,3)$
4. $(1,5)$
5. $(-3,1)$