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.

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!