Question

name: jason camacho
period: 2

1. reflect triangle abc with a(3, - 0, b(1, - 5), and c(-2, - 2) in the x - axis. what are the coordinates of b?
2. reflect square jklm with j(1, 0), k(0, 5), l(7, 0) and m(2, - 0) in the y - axis. what are the coordinates of m?
3. reflect parallelogram efgh with e(-4, 5), f(3, 6), g(2, 3), and h(-5, 2) in the x - axis. what are the coordinates of f?
4. translate rhombus rstu with r(4, 6), s(3, 7), t(2, 3), and u(-2, 2) under the rule (x, y)→(x + 5, y - 3). what are the coordinates of r?
5. translate triangle xyz with x(-4, 3), y(3, - 0) and z(-5, - 0) under the rule (x, y)→(x + 2, y - 6). what are the coordinates of y?
6. rotate rectangle cdef with c(-4, 0), d(1, - 0, e(-3, - 7) and f(-6, - 6) 90° counterclockwise about the origin. what are the coordinates of e?
7. rotate trapezoid mnop with m(3, - 2), n(6, - 2), o(8, - 5) and p(1, - 5) 180° about the origin. what are the coordinates of o?
8. rotate triangle pqr with p(-1, - 3), q(-5, - 7) and r(-7, - 3) 270° counterclockwise about the origin. what are the coordinates of p?
9. dilate triangle klm with k(2, 0), l(3, - 0) and m(4, 0) with using a scale factor of 2. what are the coordinates of k?
10. dilate rectangle wxyz with w(3, 9), x(9, 9), y(9, 6) and z(3, 6) using a scale factor of 1/3. what are the coordinates of y?
11. reflect square stuv with s(-4, 4), t(1, 0), u(1, 3), and v(2, 1) in the x - axis. what are the coordinates of v?
12. reflect triangle lmn with l(3, 10), m(8, 5), and n(5, 0) in the y - axis. what are the coordinates of m?
13. 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?
14. translate trapezoid vwxz with v(-1, 0), x(3, 0), w(7, - 3) and z(-1, - 3) under the rule (x, y)→(x + 2, y + 8). what are the coordinates of z?
15. 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?
16. rotate parallelogram jklm with j(1, - 7), k(2, - 3), l(8, - 1), and m(7, - 5) 90° counterclockwise about the origin. what are the coordinates of k?
17. rotate rectangle defg with d(-9, 5), e(-4, 10), f(-2, 8), and g(-7, 3) 180° about the origin. what are the coordinates of g?
18. rotate triangle tuv with t(8, 8), u(6, 3), and v(2, 9) 270° counterclockwise about the origin. what are the coordinates of u?
19. dilate square ghij with g(-8, 4), h(-2, 4), i(-2, - 2) and j(-8, - 2) using a scale factor of 1/2. what are the coordinates of g?
20. dilate triangle bcd with b(-4, - 2), c(0, 2), and d(2, - 0) using a scale factor of 5/2. what are the coordinates of d?

Explanation:

Step1: Recall transformation rules

• Reflection over x - axis: $(x,y)\to(x, - y)$
• Reflection over y - axis: $(x,y)\to(-x,y)$
• Translation: $(x,y)\to(x + a,y + b)$ where $a$ and $b$ are the amounts of horizontal and vertical shift respectively
• Rotation 90° counter - clockwise about the origin: $(x,y)\to(-y,x)$
• Rotation 180° about the origin: $(x,y)\to(-x,-y)$
• Rotation 270° counter - clockwise about the origin: $(x,y)\to(y,-x)$
• Dilation with scale factor $k$: $(x,y)\to(kx,ky)$

Step2: Solve problem 6

Rectangle $CDEF$ with $E(-3,-7)$ is rotated 90° counter - clockwise about the origin. Using the rule $(x,y)\to(-y,x)$, for point $E(-3,-7)$, we have $x=-3$ and $y = - 7$. Then the new coordinates are $E'(7,-3)$

Step3: Solve problem 7

Trapezoid $MNOP$ with $O(8, - 5)$ is rotated 180° about the origin. Using the rule $(x,y)\to(-x,-y)$, for point $O(8,-5)$, the new coordinates are $O'(-8,5)$

Step4: Solve problem 8

Triangle $PQR$ with $P(-1,-3)$ is rotated 270° counter - clockwise about the origin. Using the rule $(x,y)\to(y,-x)$, for point $P(-1,-3)$, the new coordinates are $P'(-3,1)$

Step5: Solve problem 9

Triangle $KLM$ with $K(-2,0)$ is dilated with a scale factor of 2. Using the rule $(x,y)\to(kx,ky)$ where $k = 2$, for point $K(-2,0)$, the new coordinates are $K'(-4,0)$

Step6: Solve problem 10

Rectangle $WXYZ$ with $Y(9,6)$ is dilated with a scale factor of $\frac{1}{3}$. Using the rule $(x,y)\to(kx,ky)$ where $k=\frac{1}{3}$, for point $Y(9,6)$, the new coordinates are $Y'(3,2)$

Step7: Solve problem 11

Square $STUV$ with $V(2,1)$ is reflected over the x - axis. Using the rule $(x,y)\to(x,-y)$, for point $V(2,1)$, the new coordinates are $V'(2,-1)$

Step8: Solve problem 12

Triangle $LMN$ with $M(8,5)$ is reflected over the y - axis. Using the rule $(x,y)\to(-x,y)$, for point $M(8,5)$, the new coordinates are $M'(-8,5)$

Step9: Solve problem 13

Rhombus $ABCD$ with $C(-4,3)$ is reflected over the y - axis. Using the rule $(x,y)\to(-x,y)$, for point $C(-4,3)$, the new coordinates are $C'(4,3)$

Step10: Solve problem 14

Trapezoid $VWXZ$ with $Z(-4,-3)$ is translated under the rule $(x,y)\to(x + 2,y+8)$. For point $Z(-4,-3)$, we have $x=-4$ and $y=-3$. Then $x'=-4 + 2=-2$ and $y'=-3 + 8 = 5$. So $Z'(-2,5)$

Step11: Solve problem 15

Triangle $QRS$ with $Q(4,7)$ is translated under the rule $(x,y)\to(x - 7,y-6)$. For point $Q(4,7)$, we have $x = 4$ and $y = 7$. Then $x'=4-7=-3$ and $y'=7 - 6=1$. So $Q'(-3,1)$

Step12: Solve problem 16

Parallelogram $JKLM$ with $K(2,-3)$ is rotated 90° counter - clockwise about the origin. Using the rule $(x,y)\to(-y,x)$, for point $K(2,-3)$, the new coordinates are $K'(3,2)$

Step13: Solve problem 17

Rectangle $DEFG$ with $G(-7,3)$ is rotated 180° about the origin. Using the rule $(x,y)\to(-x,-y)$, for point $G(-7,3)$, the new coordinates are $G'(7,-3)$

Step14: Solve problem 18

Triangle $TUV$ with $U(6,3)$ is rotated 270° counter - clockwise about the origin. Using the rule $(x,y)\to(y,-x)$, for point $U(6,3)$, the new coordinates are $U'(3,-6)$

Step15: Solve problem 19

Square $GHIJ$ with $G(-8,4)$ is dilated with a scale factor of $\frac{1}{2}$. Using the rule $(x,y)\to(kx,ky)$ where $k=\frac{1}{2}$, for point $G(-8,4)$, the new coordinates are $G'(-4,2)$

Step16: Solve problem 20

Triangle $BCD$ with $D(2,-4)$ is dilated with a scale factor of $\frac{5}{2}$. Using the rule $(x,y)\to(kx,ky)$ where $k=\frac{5}{2}$, for point $D(2,-4)$, we have $x = 2$ and $y=-4$. Then $x'=\frac{5}{2}\times2 = 5$ and $y'=\frac{5}{2}\times(-4)=-10$. So $D'(5,-10)$

Answer:

1. $(7,-3)$
2. $(-8,5)$
3. $(-3,1)$
4. $(-4,0)$
5. $(3,2)$
6. $(2,-1)$
7. $(-8,5)$
8. $(4,3)$
9. $(-2,5)$
10. $(-3,1)$
11. $(3,2)$
12. $(7,-3)$
13. $(3,-6)$
14. $(-4,2)$
15. $(5,-10)$