Question

Quadrilateral FLAG has coordinates F(1,5), L(6,3), A(3,-1), and G(-2,1). Which

statement is true?
Quadrilateral FLAG is a rhombus because all sides are congruent.
Quadrilateral FLAG is a parallelogram because opposite sides are parallel.
Quadrilateral FLAG is only a quadrilateral because no sides are congruent and no
sides are parallel.
Quadrilateral FLAG is a trapezoid because only one pair of sides are parallel.

Answer 1

Quadrilateral FLAG has coordinates F(1,5), L(6,3), A(3,-1), and G(-2,1). Which

statement is true?

Quadrilateral FLAG is a rhombus because all sides are congruent.

Quadrilateral FLAG is a parallelogram because opposite sides are parallel.

Quadrilateral FLAG is only a quadrilateral because no sides are congruent and no

sides are parallel.

Quadrilateral FLAG is a trapezoid because only one pair of sides are parallel.

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Answer 2

• B. Quadrilateral FLAG is a parallelogram because opposite sides are parallel.

Explanation:

Refer to attached.

Plot the point and connect in order FLAG.

We see

• FL ║ GA
• GF ║ AL
• FA and GL are not perpendicular

All the above can be confirmed by calculating the slopes:

• m(FL) = (3 - 5)/(6 - 1) = -2/5
• m(GA) = (1 + 1)/(-2-3) = -2/5
• These are same.

• m(GF) = (5 - 1)/(1 + 2) = 4/3
• m(AL) = (3 + 1)/(6 - 3) = 4/3
• These are same

• m(FA) = (-1 - 5)/(3 - 1) = -3
• m(GL) = (3 - 1)/(6 +2) = -1/4
• These are negative but not reciprocal

The quadrilateral is a parallelogram.

Correct choice is B