Problema Solution
Quadrilateral ABCD has coordinates A (3, -5), B (5, -2), C (10, -4), D (8, -7). Quadrilateral ABCD is a ____
a) rectangle because opposite sides are congruent and adjacent sides are perpendicular
b) square because all four sides are congruent and adjacent sides are perpendicular
c) parallelogram because opposite sides are congruent and adjacent sides are not perpendicular
d)rhombus because all four sides are congruent and adjacent sides are not perpendicular
Answer provided by our tutors
slope of line A:B = (-2+5)/(5-3) = 3/2
slope of line C:D = (-7+4)/(8-10) = -3/-2 = 3/2
lines A:B and C:D are parallel
slope of line B:C = (-4+2)/(10-5) = -2/5
slope of line D:A = (-5+7)/(3-8) = 2/-5 = -2/5
lines B:C and D:A are parallel
Bx - Ax = 5-3 = 2
Cx - Dx = 10-8 = 2
Cy - By = -4+2 = -2
Dy - Ay = -7+5 = -2
Quadrilateral ABCD is a parallelogram