Question

Choose the best selection for the
quadrilateral with vertices at the
following points:
(0,0), (1,3), (5,0), (6,3)
Hint: Start by graphing the points.
Distance Formula: d= V(x2 – x1)2 + (y2 - y1)2
A. Rectangle
B. Trapezoid
C. Rhombus
D. Parallelogram

Answer 1

The shape of the given quadrilateral is given by plotting the given points

on a graph paper.

The correct response;

• D. Parallelogram

Method by which the above response is obtained

The given points are;

(0, 0), (1, 3), (5, 0), (6, 3)

The quadrilateral is therefore;

A(0, 0), B(1, 3), C(5, 0), D(6, 3)

Distance formula

Distance formula is d = √((x₂ - x₁)² + (y₂ - y₁)²)

The lengths of the sides are;

AB = √((1 - 0)² + (3 - 0)²) = √(10)

BC = √((5 - 1)² + (0 - 3)²) = 5

CD = √((6 - 5)² + (3 - 0)²) = √(10)

AD = √((6 - 0)² + (3 - 0)²) = 3·√5

However, by plotting the points, we have;

E(0, 0), F(1, 3), G(6, 3), H(5, 0)

Which gives;

EF = √(10)

FG = √( (6 - 1)² + (3 - 3)²) = 5

GH = √((5 - 6)² + (0 - 3)²) = √10

EH = 5

Therefore, the opposite sides are equal

EF = GH

FG = EH

Slope of EF = (3)/(1) = 3

Slope of GH = (3 - 0)/(6 - 5) = 3

Slope of FG = (3 - 3)/(6 - 1) = 0

Slope of EH = (0 - 0)/(5 - 0) = 0

Therefore, the slope of the opposite sides are equal, and the opposite

sides are parallel.

The slopes of the adjacent side are not the negative inverse of the other.

Therefore, the quadrilateral is a parallelogram

• The correct option is D. Parallelogram

Learn more about parallelograms here:

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