Answer:
120 cm
Step-by-step explanation:
One way to tackle this is by getting another sheet of paper and drawing it out, then counting up the total of the sides. If you draw it, you can see that you're dealing with a rectangle; two sides of length 12 and two sides of length 8. If you don't like drawing or don't want to in this case, another way to get the answer is by knowing one vertex is at (0, 0), so the next vertex (0, 8), would create a side that's exactly 8 units long. Kind of the same, you know from (0, 0), you also have a point (12, 0), so drawing that would create a side that's 12 units long. All in all, to get the perimeter in units, you have 12 + 12 + 8 + 8 = 40.
The problem says it wants the amount of wood in centimeters needed for the perimeter. What we just found was the perimeter in generic units, so if the problem says every "grid square", or unit, is 3 centimeters long, then all you have to do is take our result 40 and multiply it by 3 to get the number of centimeters. Your perimeter in centimeters would be 120 cm.
Answer:
By definition, a parallelogram is a figure that has opposite sides parallel or it has two pairs of sides that are parallel. Based on the given figure above, the additional facts that would guarantee that JKLM is a parallelogram are the following: JK= 8 and JM= 12 and JK= 8 and JK is parallel to LM. Hope this answer helps.
Step-by-step explanation:
The explanation for this is one of my favorite pieces of mathematical reasoning. First, let's thing about distance; what's the shortest distance between two points? <em>A straight line</em>. If we just drew a straight line between A and B, though, we'd be missing a crucial element of the original problem: we also need to pass through a point on the line (the "river"). Here's where the mathemagic comes in.
If we take the point B and <em>reflect it over the line</em>, creating the point B' (see picture 1), we can draw a line straight from A to B' that passes through a point on the line. Notice the symmetry here; the distance from the intersection point to B' is<em> the same as its distance to B</em>. So, if we reflect that segment back up, we'll have a path to B, and because it came from of the line segment AB', we know that it's <em>the shortest possible distance that includes a point on the line</em>.
If we apply this same process to our picture, we see that the line segment AB' crosses the line 
at the point (1, 1)
