Answer:
The quadrilateral is a rhombus
Step-by-step explanation:
Prove Quadrilateral P(-2, 3) L( 2, 6) U (7,6) S(3, 3) Is a rhombus
A rhombus is a quadrilateral with all its sides equal to each other.
We prove this using the formula
√(x2 - x1)² + (y2 - y1)²
When given vertices (x1, y1) and (x2, y2)
For sides PL
P(-2, 3) L( 2, 6)
√(2 - (-2))² + (6 - 3)²
= √4² + 3²
= √16 + 9
= √25
= 5 units
For sides LU
L( 2, 6) U (7,6)
√(7 - 2)² + (6 - 6)²
= √5²
= √25
= 5 units
For side US
L( 2, 6) U (7,6)
= √(7 - 2)² + (6 - 6)²
= √5² + 0²
= √25
= 5 units
P(-2, 3), S(3, 3)
= √(3 - (-2))² + (3 - 3)²
= √5² + 0²
= √25
= 5 units
From the above calculation,
PL = LU = US = PS = 5 units
Hence, the above quadrilateral is a rhombus
