Aquadrilateral has vertices a(4, 9), b(2, 5), c(8, 2), and d(10, 6). which statement about the quadrilateral is true?
(a) abcd is a parallelogram with non-perpendicular adjacent sides.
(b) abcd is a trapezoid with only one pair of parallel sides.
(c) abcd is a rectangle with noncongruent adjacent sides.
(d) abcd is a square.
(e) abcd is a rhombus with non-perpendicular adjacent sides.

(C) ABCD is a rectangle with noncongruent adjacent sides.

Step-by-step explanation:

Here , A(4, 9), B(2, 5), C(8, 2), and D(10, 6),

Thus, by the distance formula,

Similarly,

,

,

Hence, for the quadrilateral,

AB = CD and BC = DA ---------(1)

Now, the slope of AB

the slope of BC

Slope of AB × Slope of BC = 2 × -1/2 = -1

⇒ Sides AB and BC are perpendicular to each other ----- (2)

Now, the slope of CD

the slope of DA

Slope of CD × Slope of DA = 2 × -1/2 = -1

⇒ Sides CD and DA are perpendicular to each other ----- (3)

Hence, from equations (1), (2) and (3),

The quadrilateral ABCD is a rectangle with non congruent adjacent sides.

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