Question

4 q6) i can describe the changes to the x- and y- coordinates of a figure after either dilation, translation, rotation or reflection. (8.g.a.3) translations 6. rectangle abcd has vertices a(-6, 1), b(-6, 4), c(-2, 4), & d(-2, 1). graph abcd by translating right 2 and down 4. write the coordinates of the image abcd after the translation. a: ____ b: __ c: __ d: ____

Explanation:

Step1: Recall translation rules

For a translation right \( h \) units and down \( k \) units, the rule is \((x,y)\to(x + h,y - k)\). Here, \( h = 2 \) (right 2) and \( k = 4 \) (down 4), so the rule is \((x,y)\to(x + 2,y - 4)\).

Step2: Find \( A' \)

Given \( A(-6,1) \), apply the rule: \( x=-6 + 2=-4 \), \( y = 1-4=-3 \). So \( A'(-4,-3) \).

Step3: Find \( B' \)

Given \( B(-6,4) \), apply the rule: \( x=-6 + 2=-4 \), \( y = 4-4=0 \). So \( B'(-4,0) \).

Step4: Find \( C' \)

Given \( C(-2,4) \), apply the rule: \( x=-2 + 2=0 \), \( y = 4-4=0 \). So \( C'(0,0) \).

Step5: Find \( D' \)

Given \( D(-2,1) \), apply the rule: \( x=-2 + 2=0 \), \( y = 1-4=-3 \). So \( D'(0,-3) \).

Answer:

\( A'(-4,-3) \)
\( B'(-4,0) \)
\( C'(0,0) \)
\( D'(0,-3) \)