Question

draw the following quadrilateral after a translation 2 units to the left and 3 units down.

Explanation:

Step1: Identify original vertices

Original quadrilateral vertices:
$(1, 4)$, $(4, 2)$, $(1, -4)$, $(-2, -3)$

Step2: Apply translation rule

Translation: $(x,y) \to (x-2, y-3)$

• For $(1,4)$: $(1-2, 4-3) = (-1, 1)$
• For $(4,2)$: $(4-2, 2-3) = (2, -1)$
• For $(1,-4)$: $(1-2, -4-3) = (-1, -7)$
• For $(-2,-3)$: $(-2-2, -3-3) = (-4, -6)$

Step3: Plot new vertices

Plot $(-1, 1)$, $(2, -1)$, $(-1, -7)$, $(-4, -6)$

Step4: Connect new vertices

Connect the 4 translated points in order to form the translated quadrilateral.

Answer:

The translated quadrilateral has vertices at $(-1, 1)$, $(2, -1)$, $(-1, -7)$, and $(-4, -6)$. When these points are connected in sequence, they form the translated figure.