The point A(1-2) B(2,3) C(K,2) and d (-4,-3) ar the vortices of a parallogram find the value of k
Answers
Answer:
K=1
Step-by-step explanation:
Given: A(1-2) B(2,3) C(K,2) and d (-4,-3) are the vertices of a parallelogram
==>AB=CD
Now,
By distance formula,
AB=√[(X1-X2)²+(Y1-Y2)²]
=√[(1-2)² + (-2-3)²]
=√[1+25]
=√26
Now,
By distance formula,
cd=√[(X1-X2)²+(Y1-Y2)²]
=√[(K-(-4))² + (-2-(-3))²]
=√[(K+4)² + 1]
AB=CD
==>√26=√[(K+4)² + 1]
==>26=K²+16+8K+1
==>K²+8K-9=0
==>K² + 9K - 1K -9=0
==>K(K+9) -1(K+9) =0
==>K=1, siNCE K CANNOT BE NEGATIVE
Answer:
Step-by-step explanation:
Given: A(1-2) B(2,3) C(K,2) and d (-4,-3) are the vertices of a parallelogram
==>AB=CD
Now,
By distance formula,
AB=√[(X1-X2)²+(Y1-Y2)²]
=√[(1-2)² + (-2-3)²]
=√[1+25]
=√26
Now,
By distance formula,
cd=√[(X1-X2)²+(Y1-Y2)²]
=√[(K-(-4))² + (-2-(-3))²]
=√[(K+4)² + 1]
AB=CD
==>√26=√[(K+4)² + 1]
==>26=K²+16+8K+1
==>K²+8K-9=0
==>K² + 9K - 1K -9=0
==>K(K+9) -1(K+9) =0
==>K=1, SINCE K CANNOT BE NEGATIVE