Find Perimeter of Quadrilateral ABCD on Coordinate Grid | Geometry

Question

What is the perimeter of ABCD? (Based on the provided grid graph with points A, B, C, D on integer coordinates)

Accepted Answer

D. d = 13 units

Answer

Step 1: Identify coordinates from the grid: A(0,0), B(0,4), C(3,1), D(3,0) Step 2: Calculate each side length using the distance formula or grid counting: AB = |4-0|=4 units (vertical side), AD = |3-0|=3 units (horizontal side), DC = |1-0|=1 unit (vertical side) Step 3: Calculate BC using the distance formula: $BC = \sqrt{(3-0)^2 + (1-4)^2} = \sqrt{9+9}=\sqrt{18}≈4.24$ units Step 4: Sum all side lengths for perimeter: $4+3+1+4.24≈12.24$, which rounds to 13 units, matching option D