Question

select the correct answer from each drop - down menu.
quadrilateral abcd is translated 7 units down and 2 units to the right.
the length of side ab of the original quadrilateral is 3 units. after the translation, the length of side ab will
increase, decrease, remain the same

Explanation:

Step1: Identify coordinates of A and B

From the graph, let's assume the coordinates of point \( A \) are \( (2, 6) \) and point \( B \) are \( (5, 6) \) (since they have the same y - coordinate, so the line AB is horizontal).

Step2: Calculate length of AB

The distance formula between two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For horizontal line (\( y_1 = y_2 \)), the formula simplifies to \( d=\vert x_2 - x_1\vert \). So \( AB=\vert5 - 2\vert= 3 \) units.

Step3: Effect of translation on length

Translation is a rigid transformation. Rigid transformations (like translation, rotation, reflection) do not change the side lengths of a figure. So after translating the quadrilateral 7 units down and 2 units to the right, the length of AB will remain the same.

Answer:

The length of side AB of the original quadrilateral is 3 units. After the translation, the length of side AB will remain the same.