Question

t and d are points on a polygon. t d are points of the polygon under a translation. determine the translation. write your answer as ⟨x,y⟩.
t(-6,7), t(-3,6)
d(-10, -10), d(-7, -11)
show your work here

Explanation:

Step1: Find x - translation for T

To find the x - component of the translation, we use the formula for the translation of a point \((x,y)\) to \((x',y')\) which is \(x'=x + a\) (where \(a\) is the x - translation) and \(y'=y + b\) (where \(b\) is the y - translation). For point \(T(-6,7)\) and \(T'(-3,6)\), we solve for \(a\) using \(x'\) and \(x\) values. So, \(-3=-6 + a\). Solving for \(a\), we add 6 to both sides: \(a=-3 + 6=3\).

Step2: Find y - translation for T

Using the y - values of \(T\) and \(T'\), we have \(6 = 7 + b\). Solving for \(b\), we subtract 7 from both sides: \(b=6 - 7=-1\).

Step3: Verify with point D

For point \(D(-10,-10)\) and \(D'(-7,-11)\), we check the x - translation: \(-7=-10 + a\). Substituting \(a = 3\) (from step 1), we get \(-10+3=-7\), which is correct. For the y - translation: \(-11=-10 + b\). Substituting \(b=-1\) (from step 2), we get \(-10-1=-11\), which is also correct.

Answer:

\(\langle3,-1
angle\)