Question

name:
17 △pqr has vertices p(6,6), q(0,0), and r(-2,2). the triangle is translated left 2 units and down 1 unit. without graphing, find the coordinates of p, q, and r.
a. p(4,7), q(-2,1), r(-4,3)
c. p(4,5), q(-2,-1), r(-4,1)
b. p(8,5), q(2,-1), r(0,1)
d. p(8,7), q(2,1), r(0,3)
reflections

1. a reflection is an isometry.

a. true
b. false
19 what is the rule for reflecting a shape over the x - axis.
a. (x,y)→(-x,-y) b. (x,y)→(y,x) c. (x,y)→(-x,y) d. (x,y)→(x,-y)
20 point a(9,-4) is reflected over the y - axis. write the coordinates of a.
a. (-9,-4) b. (9,-4) c. (9,4) d. (-9,4)

1. △abc has vertices a(-1,-2), b(-4,-4), and c(-3,-5). graph △abc and its image after a reflection over the x - axis. name the coordinates of the vertices of the reflected triangle. answer on short answer sheet not bubble sheet.
2. △abc has vertices a(-2,-3), b(-4,-6), and c(-5,-2). graph △abc and its image after a reflection over the y = 2 line. name the coordinates of the vertices of the reflected triangle. answer on short answer sheet not bubble sheet.

rotations

1. a rotation is an isometry.

a. true
b. false

1. out of the degrees listed below which will produce the exact... clockwise and counterclockwise?

a. d. all of the above
image of △dfh after a rotation of 90° about the origin. answer on short answer sheet not bubble sheet. ccw

Explanation:

Step1: Understand the translation rule

When a point \((x,y)\) is translated left \(a\) units and down \(b\) units, the new coordinates are \((x - a,y - b)\). Here \(a = 2\) and \(b=1\).

Step2: Find \(P'\)

For point \(P(6,6)\), using the rule \(x'=6 - 2=4\) and \(y'=6 - 1 = 5\), so \(P'(4,5)\).

Step3: Find \(Q'\)

For point \(Q(0,0)\), using the rule \(x'=0 - 2=-2\) and \(y'=0 - 1=-1\), so \(Q'(-2,-1)\).

Step4: Find \(R'\)

For point \(R(-2,2)\), using the rule \(x'=-2 - 2=-4\) and \(y'=2 - 1 = 1\), so \(R'(-4,1)\).

Answer:

C. \(P'(4,5),Q'(-2,-1),R'(-4,1)\)