Question

If trapezoid jklm is translated using the rule (x, y) → (x 3, y − 3) and then translated using the rule (x, y) → (x 2, y − 2) to create trapezoid j″k″l″m″, what is the location of k″?

Answer 1

The location of k″ is 5 units to the right and 5 units down from the original point k.

Step-by-step explanation:

To find the location of k″, we need to apply the two translation rules to each point of the trapezoid. Let's start with the first translation rule that moves each point 3 units to the right and 3 units down.

Given that the original point k has coordinates (x,y), its new coordinates after the first translation will be (x+3,y-3).

Now, let's apply the second translation rule that moves each point 2 units to the right and 2 units down. So, the final coordinates of k″ will be (x+3+2,y-3-2) = (x+5,y-5). Therefore, the location of k″ is 5 units to the right and 5 units down from the original point k.