Question

1. the vertices of △abc are a(2,1), b(3,4), and c(1,3). if △abc is translated 1 unit down and 3 units to the left to create △def, what are the coordinates of the vertices of △def?

a. d(0,1), e(1,2), f(1,3)
b. d(0, - 1), e(0,3), f(-2,-2)
c. d(-2,2), e(0,3), f(-1,0)
d. d(-1,0), e(0,3), f(-2,2)

1. if triangle abc is rotated 180 degrees about the origin, what are the coordinates of a?

a. (-5,-4)
b. (-5,4)
c. (-4,5)
d. (-4,-5)

1. trapezoid abcd below is to be translated to trapezoid abcd by the following motion rule: (x,y)→(x + 3,y - 4)

what will be the coordinates of vertex c?
a. (1,-3)
b. (2,1)
c. (6,1)
d. (8,-3)

Explanation:

Step1: Recall translation rule

A translation 1 unit down and 3 units to the left has the rule \((x,y)\to(x - 3,y - 1)\).

Step2: Translate point A

For point \(A(2,1)\), \(x=2\) and \(y = 1\). Using the rule \((x-3,y - 1)\), we get \(A'=(2 - 3,1-1)=(-1,0)\).

Step3: Translate point B

For point \(B(3,4)\), \(x = 3\) and \(y=4\). Using the rule \((x - 3,y-1)\), we get \(B'=(3 - 3,4 - 1)=(0,3)\).

Step4: Translate point C

For point \(C(1,3)\), \(x = 1\) and \(y = 3\). Using the rule \((x-3,y - 1)\), we get \(C'=(1 - 3,3-1)=(-2,2)\).

Answer:

D. \(D(-1,0), E(0,3), F(-2,2)\)