Question

determine a and b so that figure abcd is a parallelogram.
a =

b =

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite sides are equal. The x - coordinates of opposite vertices have the same difference. For side AB and CD, the x - coordinate of B is 5 and of A is 0, the x - coordinate of D is a and of C is 2. So, \(5 - 0=a - 2\).
\[5=a - 2\]

Step2: Solve for a

Add 2 to both sides of the equation \(5=a - 2\).
\[a=5 + 2=7\]

Step3: Use y - coordinate property

For the y - coordinates, the y - coordinate of B is 3 and of A is 0, the y - coordinate of D is 3 and of C is b. So, \(3-0 = 3 - b\).
\[3=3 - b\]

Step4: Solve for b

Subtract 3 from both sides: \(0=-b\), so \(b = 0\).

Answer:

a = 7
b = 0