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5. The coordinates of this parallelogram are given. Determine if each statement is True or False. * 20 points (2, 5) (P. 5) (-1, 1) (m, n) True False G B H The length of the longer side is p-2. The length of the longer side is n+1. The short side is 4 units in length. n = 5 m>n С 1 D J E K F L p = 2

5. The coordinates of this parallelogram are given. Determine if each statement is-example-1
User Jensdc
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- The length of the longer side is p - 2 as we are subtracting the x-coordinates. So the first statement is true.

- The length of the longer side is not n+1 as you have to subtract -1 from m to find the length of the longer side. So the second statement is false.

- The short side can be found with the following calculation.


\begin{gathered} s=\sqrt[]{\mleft(5-1\mright)^2+(2-(-1))^2}\text{ (Using the pythagorean theorem with a triangle formed by drawing the heigth of the parallelogram )} \\ s=\sqrt[]{(5-1)^2+(2+1))^2}\text{ (Using the sign rules)} \\ s=\sqrt[]{(4)^2+(3))^2}\text{ (Adding and subtracting)} \\ s=\sqrt[]{16^{}+9}\text{ (Raising both numbers to the power of 2)} \\ s=\sqrt[]{25}\text{ (Adding)} \\ s=5\text{ (Taking the square root)} \end{gathered}

We can see that the short side is not four units in length. The third statement is false.

- We see that n is equal to 1 as the two points that form the base must have the same y-coordinate. The fourth statement is false.

- We see that m must be greater than 2 as the point (-1,1) is more distanced to the point (m,n) than to the point (2,5) on the x-axis. So m>n (n=1) . The fifth statement is true.

- We see that p is greater than 2 as the point (p,5) is to the right of the point (2,5). So the sixth statement is false.

User BustedSanta
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