Answer:
From the calculation,
KL = 13
NM = √65
Hence KL ≠ NM
Therefore, the quadrilateral KLMN is not a Parallelogram.
Step-by-step explanation:
K(–5, –4), L(0, 8), M(7, 4), and N(8, –4)
Where we have vertices, (x1, y1) , (x2, y2)
We use the formula
√(x2 - x1)² + (y2 - y1)²
Side KL = K(–5, –4), L(0, 8)
√(x2 - x1)² + (y2 - y1)²
√(0 - (-5))² + (8 - (-4))²
√ 5² + 12²
√25 + 144
= √169
= 13
Side KN = K(–5, –4), N(8, –4)
√(x2 - x1)² + (y2 - y1)²
√(8 -(-5))² + (-4 - (-4))²
√13² + 0²
√169
=13
Side MN = M(7, 4), N(8, –4)
√(x2 - x1)² + (y2 - y1)²
√(8 -7)² + (-4 - 4)²
√1² + (-8)²
√1 + 64
√65
Side LM = L(0, 8), M(7, 4),
√(x2 - x1)² + (y2 - y1)²
√(7-0)² + (4 - 8)²
√(49)² +(-4)²
√ 49 + 16
√65
We were asked in the above question to prove that the quadrilateral with the given vertices is not a Parallelogram.
One of the characteristics of a Parallelogram is that the opposite sides are parallel and congruent to one another. This means that, the opposite sides are similar .
For the Quadrilateral KLMN above to be a Parallelogram, this means
KL = NM
From the above calculation,
KL = 13
NM = √65
Hence KL ≠ NM
Therefore, the quadrilateral KLMN is not a Parallelogram.
