- 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.