Question

name:
geometry chapter 4 review

1. graph \\( \triangle a b c \\) with vertices \\( a ( 2,1 ) \\), \\( b ( - 1,2 ) \\) and \\( c ( - 2, - 1 ) \\) and its image after the following sequence of

transformations.
translation: \\( ( x, y ) \
ightarrow ( x - 1, y - 3 ) \\)
translation: \\( ( x, y ) \
ightarrow ( x + 4, y + 3 ) \\)

write a rule for the translation that maps each figure to its image.
2.
3.

1. if \\( \triangle x y z \\) is the image of a translation of \\( \triangle a b c, a \\) is at \\( ( 1,1 ) \\) and \\( x \\) is at \\( ( 5, - 2 ) \\), what translation rule

maps \\( \triangle a b c \\) to \\( \triangle x y z \\) ?
a. \\( ( x, y ) \
ightarrow ( x + 4, y - 3 ) \\)
b. \\( ( x, y ) \
ightarrow ( x - 4, y - 3 ) \\)
c. \\( ( x, y ) \
ightarrow ( x + 4, y + 2 ) \\)
d. \\( ( x, y ) \
ightarrow ( x + 4, y - 2 ) \\)

1. triangle \\( a b c \\) with coordinates \\( a ( 3, - 2 ) , b ( 3,4 ) \\), and \\( c ( 6,5 ) \\) it is translated following the rule \\( ( x , y ) \

ightarrow \\)
\\( ( x + 3 , y - 8 ) \\). what will be the resulting coordinates of the vertices of the transformed triangle \\( a ^ { prime } , b ^ { prime } \\),
\\( c ^ { prime } \\) ?
a. \\( a ( 6 , - 10 ) , b ( 6 , - 4 ) \\), and \\( c ( 9 , - 3 ) \\)
b. \\( a ( 6,2 ) , b ( 3,12 ) \\), and \\( c ( 9,13 ) \\)
c. \\( a ( 0 , - 10 ) , b ( 0 , - 4 ) \\), and \\( c ( 3 , - 3 ) \\)
d. \\( a ( 0,2 ) , b ( 0,12 ) \\), and \\( c ( 3,13 ) \\)

Explanation:

Step1: Find the change in x - coordinate

For point \(A(1,1)\) and \(X(5, - 2)\), the change in \(x\) is \(5 - 1=4\).

Step2: Find the change in y - coordinate

The change in \(y\) is \(-2 - 1=-3\).

Answer:

A. \((x,y)\to(x + 4,y - 3)\)