A common strategy when finding the area of a polygon while you're only given the coordinates is to employ the shoelace formula. To start, we have to order the coordinates either clockwise or counterclockwise ( see attatched for a drawing). So, now we can order the coordinates counterclockwise, adding the first entry again at the end (see second attatchment) Now we can use shoelace. When going left to right, we'll multiply the numbers and they will be positive, and we'll make those numbers negative. ( see third attatchment). After we add them up and subtract when necessary, we'll divide the whole thing by 2. Here's the math:
Part (a)
The angles would stay the same. This is because similar figures keep the same shape, but the size will shrink or grow.
A real world application is to simply move your head closer to the page and the figure will appear to get larger. The angles themselves stay the same but the side lengths will get larger.
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Part (b)
While the angles stay the same under a dilation operation, the side lengths do not. As the instructions state: "The side lengths are 3 times longer" (paraphrased).
So we multiply each side length in the diagram by 3
- DE = 3*JK = 3*4.5 = 13.5
- EF = 3*KL = 3*3 = 9
- FG = 3*LM = 3*2 = 6
- GD = 3*MJ = 3*2.5 = 7.5
Refer to the diagram below. I've used the resize feature to enlarge the image to make figure DEFG
Answer:
associatve property
Step-by-step explanation:
