In the coordinate plane, draw quadrilateral abcd with a(–5, 0), b(2, –6), c(8, 1), and d(1, 7), then demonstrate that abcd is a rectangle.

ABCD is a rectangle

Step-by-step explanation:

∵ A = (-5 , 0) , B = (2 , -6) , C = (8 , 1) , D = (1 , 7)

∵ The x-coordinate of the mid-point of AC = (-5 + 8)/2 =3/2

∵ The y-coordinate of the mid-point of AC = (0 + 1)/2 = 1/2

∴ The mid-point of AC = (3/2 , 1/2)

∵ The x-coordinate of the mid-point of BD = (2 + 1)/2 =3/2

∵ The y-coordinate of the mid-point of BD = (-6 + 7)/2 = 1/2

∴ The mid-point of BD = (3/2 , 1/2)

∴ The mid-point of AC = The mid-point of BD ⇒ (1)

∵ AC = √[(8 - -5)²+(1 - 0)² = √170

∵ BD = √[(1 - 2)²+(7 - -6)² = √170

∴ AC = BD ⇒ (2)

From (1) and (2)

AC and BD equal each other and bisects each other

∴ ABCD is a rectangle

answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,

according to egenuity the answer is

step-by-step explanation:

d. 344.22