8) Determine which points are the remaining vertex of a rectangle with an perimeter of 14 units. a) A(2,-1) and B(-2,-1) b) C(-1,-2) and D(1,-2) c) E(-2,-2) and F(2,-2) d) G(2,0) and H(-2,0)

1. Calculate the length of given sides<br /> For each pair, calculate the distance using **distance formula**: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.<br /><br />- $AB$: $d = \sqrt{(-2 - 2)^2 + (-1 + 1)^2} = \sqrt{16} = 4$<br />- $CD$: $d = \sqrt{(1 + 1)^2 + (-2 + 2)^2} = \sqrt{4} = 2$<br />- $EF$: $d = \sqrt{(2 + 2)^2 + (-2 + 2)^2} = \sqrt{16} = 4$<br />- $GH$: $d = \sqrt{(-2 - 2)^2 + (0 - 0)^2} = \sqrt{16} = 4$<br /><br />2. Determine possible rectangle sides<br /> A rectangle has two pairs of equal lengths. Check if any combination of these distances can form a rectangle with perimeter 14.<br /><br />- Perimeter formula: **$P = 2(l + w)$**, where $l$ and $w$ are lengths of adjacent sides.<br />- Possible combinations:<br /> - $AB = 4$, $CD = 2$: $2(4 + 2) = 12$ (not 14)<br /> - $EF = 4$, $CD = 2$: $2(4 + 2) = 12$ (not 14)<br /> - $GH = 4$, $CD = 2$: $2(4 + 2) = 12$ (not 14)<br /><br />3. Verify other combinations<br /> Check if any other combination of points can satisfy the perimeter condition.<br /><br />- No other combinations of given points result in a perimeter of 14.