Question

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and rounded to the nearest tenth.

A (−9, 3), B (−6, −1), C (2, 5), D (−5, 6)

Answer 1

Perimeter = 5 + 5 + 7.1 + 10 =27.1

area = (5 + 10)x5 / 2 = 37.5

Explanation:

Slope formula: m = (x' - x)/(y' - y)

m-AD: (6-3)/(-5 - -9) = 3/4 (I'm not detail other Other slopes)

m- BC = 3/4

m-AB = - 4/3

m-AD = m-BC AD // BC (ABCD is a Trapezoid)

m-AB = - 1 / m-BC

AB ⊥ BC

segment length formula: d = √(x' - x)² + (y' - y)²

AD = √(-5 - -9)² + (6 - 3)² = √4² + 3² = √25 = 5

DC = √50 = 7.1

BC = √100 = 10

AB = √25 = 5

Perimeter = 5 + 5 + 7.1 + 10 =27.1

area = (5 + 10)x5 / 2 = 37.5

area ABCD = (5+10)x5 / 2 =