A(1,-2) B(2,-3) C(k,2) D(4,3)are vertical of parallelogram find The value of k
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Answer: k=5 or k=3
Step-by-step explanation:
A(1,-2) B(2,-3) C(k,2) D(4,3) are vertices of a parallelogram.
Opposite sides of a parallelogram are equal,
AB=CD
By applying distance formula,
√(2-1)²+(-3+2)² = √(4-k)²+(3-2)²
√(1)²+(-1)² = √(4)²-2(k)(4)+k²+(1)²
√1+1 = √16-8k+k²+1
√2=√k²-8k+17
On squaring both sides,
2=k²-8k+17
k²-8k+15=0
k²-5k-3k+15=0
k(k-5)-3(k-5)=0
(k-5)(k-3)=0
On equation both expressions with 0,
k=5 or k=3
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