Given a length of 3h, a width of k, and a vertex at (- h,k) the length has to be parallel to the x-axis and the width has to be parallel to the y-axis.
A
Practice makes perfect
Let's plot the vertex (- h,k) in a coordinate system. We will assume that h and k are both positive numbers which places the point in the second quadrant.
Next, we will draw the length of the rectangle. Since the length is 3 h, and - h is the x-coordinate in (- h,k), we can only draw the length parallel to the x-axis. Therefore, our second vertex will also have a y-coordinate of k. As for the x-coordinate, we can draw the rectangles length both in the negative direction and in the positive direction of the x-axis. Therefore, we end up with two possibilities:
Negative direction:& - h-2h=- 4h
Positive direction:& - h+2h=2h
Let's add this to our diagram.
Next, we have to draw the width. Because a rectangle has four right angles, the width has to be drawn parallel to the y-axis. Again, there are two options, either we draw the width in the positive direction or we draw it in the negative direction of the y-axis.
Negative direction:& k-k=0
Positive direction:& k+k=2k
We end up with four possible rectangles. The labeled vertices below are the only possibilities.
The only option that is not represented in the diagram is (h,k) which is option A.
