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Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right, and from the y-coordinate if the figure is being moved up or down.
Use the formula for the area of a square.
7200 square yards
We are given a plot of land shaped like the figure in the following graph.
Translations are done by adding or subtracting values from the x-coordinate if the figure is being moved left or right, and from the y-coordinate if the figure is being moved up or down. We want to draw the image of figure ABCD after a translation 120 yards right and 100 yards up. Therefore, we will add 120 to the x-coordinate and add 100 to the y-coordinate of each vertex.
| Vertices of ABCD | (x+120,y+100) | Vertices of A'B'C'D' |
|---|---|---|
| A(20,40) | (20 + 120,40 + 100) | A'(140,140) |
| B(20,100) | (20 + 120,100 + 100) | B'(140,200) |
| C(80,100) | (80 + 120,100 + 100) | C'(200,200) |
| D(80,40) | (80 + 120,40 + 100) | D'(200,140) |
We want to find the combined area of the 2 given plots.
Area of a Square = a^2 In the formula, a is the side length of a square. We can find the side length of one plot by looking at the graph.
Therefore, a= 60. Now we substitute the value of a into the formula and calculate the area of the plot. Area of a Square = 60^2 = 3600 We got that the area of one plot equals 3600 square yards. Since both plots have equal areas, the combined area is equal to 2* 3600 = 7200 square yards.
