On a coordinate plane, a shape is plotted with vertices of (3, 1), (0, 4), (3, 7), and (6, 4). what is the area of the shape if each grid unit equals one centimeter?
Accepted Solution
A:
Let A (3, 1) B (0, 4) C(3, 7) D (6, 4)
step 1 find the distance AB d=√[(y2-y1)²+(x2-x1)²]------> dAB=√[(4-1)²+(0-3)²]-----> dAB=√18 cm
step 2 find the distance CD d=√[(y2-y1)²+(x2-x1)²]------> dCD=√[(4-7)²+(6-3)²]-----> dCD=√18 cm
step 3 find the distance AD d=√[(y2-y1)²+(x2-x1)²]------> dAD=√[(4-1)²+(6-3)²]-----> dAD=√18 cm
step 4 find the distance BC d=√[(y2-y1)²+(x2-x1)²]------> dBC=√[(7-4)²+(3-0)²]-----> dBC=√18 cm
step 5 find slope AB and CD m=(y2-y1)/(x2-x1) mAB=-1 mCD=-1 AB and CD are parallel and AB=CD
step 6 find slope AD and BC m=(y2-y1)/(x2-x1) mAD=1 mBC=1 AD and BC are parallel and AD=BC and AB and AD are perpendicular BC and CD are perpendicular
therefore the shape is a square wit length side √18 cm
area of a square=b² b is the length side of a square area of a square=(√18)²------> 18 cm²