Question

for #1-4, find the perimeter of the polygon with the given vertices. 1. g(2, 4), h(2, -3), j(-2, -3), k(-2, 4)

Explanation:

Step1: Identify the shape

The vertices are \( G(2, 4) \), \( H(2, -3) \), \( J(-2, -3) \), \( K(-2, 4) \). By plotting these points (or analyzing coordinates), we see it's a rectangle. In a rectangle, opposite sides are equal.

Step2: Calculate length of vertical side (GH or JK)

For points \( G(2, 4) \) and \( H(2, -3) \), since x - coordinates are same, the length is \( |4 - (-3)| = |7| = 7 \).

Step3: Calculate length of horizontal side (HJ or KG)

For points \( H(2, -3) \) and \( J(-2, -3) \), since y - coordinates are same, the length is \( |2 - (-2)| = |4| = 4 \).

Step4: Calculate perimeter of rectangle

The formula for the perimeter of a rectangle is \( P = 2\times (length + width) \). Here, length \( l = 7 \), width \( w = 4 \). So \( P = 2\times(7 + 4)=2\times11 = 22 \).

Answer:

22