Question

name: _ period: _ date: _
lt: i can find the coordinates of points after transformations.

1. a triangular block of concrete at a construction site, \\( \triangle a b c \\), is to be moved using a translation of 5 units to the right and 3 units down. the coordinates of a, b, and c are shown in the table below. find the coordinates of the blocks new location.

1. a triangle has coordinates a (2, 1), b (3, 2), and c (1, 4). it is transformed using the mapping rule shown in the table. complete the table and graph the preimage and image.

mapping rule: \\( ( x, y ) \
ightarrow ( x - 2, y + 3 ) \\)

Explanation:

Step1: Find the mapping rule for problem 1

For a translation of \(5\) units to the right (add \(5\) to \(x\) - coordinate) and \(3\) units down (subtract \(3\) from \(y\) - coordinate). The mapping rule is \((x,y)\to(x + 5,y-3)\)

• For point \(A(1,1)\):

\(x=1,y = 1\). New \(x\) - coordinate \(x'=1 + 5=6\), new \(y\) - coordinate \(y'=1-3=-2\). So \(A'(6,-2)\)

• For point \(B(3,1)\):

\(x = 3,y=1\). New \(x\) - coordinate \(x'=3 + 5=8\), new \(y\) - coordinate \(y'=1-3=-2\). So \(B'(8,-2)\)

• For point \(C(2,5)\):

\(x = 2,y = 5\). New \(x\) - coordinate \(x'=2+5 = 7\), new \(y\) - coordinate \(y'=5 - 3=2\). So \(C'(7,2)\)

Step2: Use the mapping rule \((x,y)\to(x - 2,y + 3)\) for problem 2

• For point \(A(2,1)\):

\(x = 2,y=1\). New \(x\) - coordinate \(x'=2-2=0\), new \(y\) - coordinate \(y'=1 + 3=4\). So \(A'(0,4)\)

• For point \(B(3,2)\):

\(x=3,y = 2\). New \(x\) - coordinate \(x'=3-2 = 1\), new \(y\) - coordinate \(y'=2+3=5\). So \(B'(1,5)\)

• For point \(C(1,4)\):

\(x = 1,y=4\). New \(x\) - coordinate \(x'=1-2=-1\), new \(y\) - coordinate \(y'=4 + 3=7\). So \(C'(-1,7)\)
The verbal description for the mapping rule \((x,y)\to(x - 2,y + 3)\) is a translation of \(2\) units to the left and \(3\) units up.

Answer:

Problem 1:

• \(A(1,1)\to A'(6,-2)\)
• \(B(3,1)\to B'(8,-2)\)
• \(C(2,5)\to C'(7,2)\)
• Mapping Rule: \((x,y)\to(x + 5,y-3)\)

Problem 2:

• \(A(2,1)\to A'(0,4)\)
• \(B(3,2)\to B'(1,5)\)
• \(C(1,4)\to C'(-1,7)\)
• Verbal Description: A translation of \(2\) units to the left and \(3\) units up.