Question

3.3 homework - reflections and translations - graded
triangle abc has vertices a(-2, 3), b(-4, 7), c(6, 8). find the coordinates of the points after a translation left 7 units and down 6 units.
a(

b(

c(

Explanation:

Step1: Recall translation rule

For a left - shift of \(a\) units and down - shift of \(b\) units, the rule for a point \((x,y)\) is \((x - a,y - b)\). Here \(a = 7\) and \(b=6\).

Step2: Translate point A

For point \(A(-2,3)\), \(x=-2\) and \(y = 3\). After translation, \(x'=-2-7=-9\) and \(y'=3 - 6=-3\). So \(A'(-9,-3)\).

Step3: Translate point B

For point \(B(-4,7)\), \(x=-4\) and \(y = 7\). After translation, \(x'=-4-7=-11\) and \(y'=7 - 6 = 1\). So \(B'(-11,1)\).

Step4: Translate point C

For point \(C(6,8)\), \(x = 6\) and \(y = 8\). After translation, \(x'=6-7=-1\) and \(y'=8 - 6=2\). So \(C'(-1,2)\).

Answer:

A'(-9,-3)
B'(-11,1)
C'(-1,2)