Question

unit 2, quiz 2: solve for unknown angles - angles in a triangle and transformations
write your answer in the appropriate space provided.

1. write the coordinates of the vertices after a translation 5 units right and 3 down. (4 pts)

s
r
t
u

1. triangle xyz with vertices x(-2,5), y(3,-1), and z(0,6) is translated so that x is at (4,2). state the coordinates of y and z. (2 pts)

y
z

1. write the coordinates of the vertices after a reflection over y axis. (4 pts)

d
e
b
c

1. c is the image of the point c after a reflection.

c(7,3)→c(-7,3)
over which axis was the point c reflected? (2 points)

1. write the coordinates of the vertices after a rotation 270° counterclockwise around the origin. graph the image and label. (4 pts)

s
t
r
u

Explanation:

1)

Step1: Determine the original coordinates

From the graph, \(S(-9,-3)\), \(R(-8,-4)\), \(T(-1,0)\), \(U(1,0)\)

Step2: Apply the translation rule \((x,y)\to(x + 5,y-3)\)

For \(S\): \(x=-9,y = - 3\), \(x+5=-9 + 5=-4\), \(y-3=-3-3=-6\), so \(S'(-4,-6)\)
For \(R\): \(x=-8,y=-4\), \(x + 5=-8+5=-3\), \(y-3=-4-3=-7\), so \(R'(-3,-7)\)
For \(T\): \(x=-1,y = 0\), \(x+5=-1 + 5=4\), \(y-3=0-3=-3\), so \(T'(4,-3)\)
For \(U\): \(x = 1,y=0\), \(x+5=1 + 5=6\), \(y-3=0-3=-3\), so \(U'(6,-3)\)

Step1: Find the translation rule

Given \(X(-2,5)\to X'(4,2)\). The translation rule is \((x,y)\to(x+6,y - 3)\) (since \(4-(-2)=6\) and \(2 - 5=-3\))

Step2: Apply the rule to \(Y\) and \(Z\)

For \(Y(3,-1)\): \(x=3,y=-1\), \(x+6=3 + 6=9\), \(y-3=-1-3=-4\), so \(Y'(9,-4)\)
For \(Z(0,6)\): \(x=0,y = 6\), \(x+6=0+6=6\), \(y-3=6-3=3\), so \(Z'(6,3)\)

Step1: Determine the original coordinates

From the graph, \(D(8,4)\), \(E(6,-1)\), \(B(8,-6)\), \(C(10,0)\)

Step2: Apply the reflection rule over \(y\)-axis \((x,y)\to(-x,y)\)

For \(D\): \(x = 8,y=4\), so \(D'(-8,4)\)
For \(E\): \(x=6,y=-1\), so \(E'(-6,-1)\)
For \(B\): \(x = 8,y=-6\), so \(B'(-8,-6)\)
For \(C\): \(x = 10,y=0\), so \(C'(-10,0)\)

Answer:

\(S'(-4,-6)\), \(R'(-3,-7)\), \(T'(4,-3)\), \(U'(6,-3)\)

2)