Question

geometry do now (11/14/25)
part one: translations - each coordinate plane below shows a preimage and its translated image.
write a sentence to describe each translation. the first problem has been completed for you.
triangle jkl was translated 4 units to the right
and 2 units up to form triangle jkl.

Explanation:

Step1: Analyze the translation of triangle DEF to D'E'F'

• Look at the \(y -\)coordinates: \(E( - 1,4)\) and \(E'( - 2,0)\), \(D( - 4,6)\) and \(D'( - 5,3)\), \(F( - 7,6)\) and \(F'( - 8,2)\).
• The change in \(y -\)coordinate: \(4 - 0=6 - 3 = 6 - 2=4\) (downward).
• The change in \(x -\)coordinate: \(-1-(-2)=-4 - (-5)=-7-(-8) = 1\) (leftward).

Step2: Analyze the translation of rectangle PQRS to P'Q'R'S'

• Look at the \(y -\)coordinates: \(P(-2,-3)\) and \(P'(-7,2)\), \(Q(0,-3)\) and \(Q'(-5,2)\), \(R(0,-6)\) and \(R'(-5,-1)\), \(S(-2,-6)\) and \(S'(-7,-1)\).
• The change in \(y -\)coordinate: \(-3 - 2=-6-(-1)=5\) (upward).
• The change in \(x -\)coordinate: \(-2-(-7)=0 - (-5)=5\) (leftward).

Step3: Analyze the translation of quadrilateral RSTU to R'S'T'U'

• Look at the \(y -\)coordinates: \(R(0,7)\) and \(R'(3,-2)\), \(S(1,7)\) and \(S'(4,-2)\), \(T(2,1)\) and \(T'(5,-5)\), \(U(-1,1)\) and \(U'(2,-5)\).
• The change in \(y -\)coordinate: \(7-(-2)=1-(-5) = 9\) (downward).
• The change in \(x -\)coordinate: \(0 - 3=1 - 4=-1 - 2=-3\) (rightward).

Answer:

• Triangle \(DEF\) was translated \(1\) unit to the left and \(4\) units down to form triangle \(D'E'F'\).
• Rectangle \(PQRS\) was translated \(5\) units to the left and \(5\) units up to form rectangle \(P'Q'R'S'\).
• Quadrilateral \(RSTU\) was translated \(3\) units to the right and \(9\) units down to form quadrilateral \(R'S'T'U'\).