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Use the coordinates to find the length of each side. Then find the perimeter of the rectangle. a. \( E(3,6), F(3,8), G(7,8), H(7,6) \) b. \( I(1,4), J(1,9), K(8,9), L(8,4) \)

Ask by Barker Mitchell. in the United States
Mar 11,2025

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**a. Rectangle with vertices \( E(3,6) \), \( F(3,8) \), \( G(7,8) \), \( H(7,6) \):** - Vertical side length: 2 - Horizontal side length: 4 - Perimeter: 12 **b. Rectangle with vertices \( I(1,4) \), \( J(1,9) \), \( K(8,9) \), \( L(8,4) \):** - Vertical side length: 5 - Horizontal side length: 7 - Perimeter: 24

Solución

**a. For rectangle with vertices \( E(3,6) \), \( F(3,8) \), \( G(7,8) \), \( H(7,6) \):** 1. **Calculate the length of the vertical side (e.g., \( EF \)):** \[ EF = |8-6| = 2 \] 2. **Calculate the length of the horizontal side (e.g., \( FG \)):** \[ FG = |7-3| = 4 \] 3. **Calculate the perimeter:** The perimeter \( P \) is given by \[ P = 2(\text{vertical side} + \text{horizontal side}) = 2(2+4) = 2(6) = 12 \] **b. For rectangle with vertices \( I(1,4) \), \( J(1,9) \), \( K(8,9) \), \( L(8,4) \):** 1. **Calculate the length of the vertical side (e.g., \( IJ \)):** \[ IJ = |9-4| = 5 \] 2. **Calculate the length of the horizontal side (e.g., \( JK \)):** \[ JK = |8-1| = 7 \] 3. **Calculate the perimeter:** The perimeter \( P \) is \[ P = 2(\text{vertical side} + \text{horizontal side}) = 2(5+7) = 2(12) = 24 \]

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To find the lengths of the sides of each rectangle, we calculate the distances between the points. For rectangle \( EFGH \): - The length (EF or HG) is the difference in the y-coordinates: \(8 - 6 = 2\). - The width (EH or FG) is the difference in the x-coordinates: \(7 - 3 = 4\). - The perimeter is calculated by adding all sides: \(2(2 + 4) = 12\). For rectangle \( IJKL \): - The length (IJ or KL) is the difference in the y-coordinates: \(9 - 4 = 5\). - The width (IL or JK) is the difference in the x-coordinates: \(8 - 1 = 7\). - The perimeter is calculated as: \(2(5 + 7) = 24\). So, the perimeters are 12 for rectangle EFGH and 24 for rectangle IJKL!

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