Question

three vertices of a parallelogram are A(-2, 3), B(6,7) and C(8, 3). Find the fourth vertex D

Answer 1

Hi,

Here is your answer,

Let us consider fourth vertex as D (a,b)

Midpoint of AC = Mid point of BD

 {(-2+8)/2,(3+3)/2} →{(6 +a)/2 , (7+b)/2}

Mid point formula→ {( x₁+x₂)/2 ,(y₁ +y₂)/2}

 {6/2 , 6/2} → {(6 +a}/2 , (7+b)/2}

6/2 → (6 +a) / 2 , 6/2 → (7+b) /2

6 → 6 +a , 6 → 7 + b

6 -6→ a  , 6 -7 → b

a →0  , b → -1


∴ The 4th vertex is {0,-1}