Question

the following set of coordinates represents which figure? . (3,-5), (5,-2), (10,-4), (8,-7). . A. parallelogram . B. rectangle . C. rhombus . D. square

Answer 1

Parallelogram

Explanation:

Answer 2

AB = √(5 -1)² + (-2 + 5)² = √(4+9) =√13
CD = √(8-7)²+(-7+4)² =√(4+9) =√13
AB = CD = √13
BC = √(25 + 4) = √29
AD = √(25 + 4) = √29
BC = AD = √29
Therefore the figure is not C ) or D ).
The question is is it a parallelogram or a rectangle.
Equation of a line through 2 points:
y - y 1 = (y2 - y1)/ (x2 - x1) ( x - x 1)
Line AB : y + 5 = 3/2 ( x - 3 )
Line AD = -2/5 ( x - 3 )
m 1 = 3/2; m 2 = -2/5
m 2 ≠ -1 / m 1
AB and AD ere not perpendicular lines.
Answer: A ) parallelogram.