Question

three vertices of a parallelogram taken in order are (-1,-6),(2,-5) and (7,2) the fourth vertex is ​

Answer 1

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Answer 2

Step-by-step explanation:

Let A(−1,−6),B(2,−5),C(7,2) and D(x,y).

AC and BD are diagonals.

So, we know that the diagonals bisect each other in parallelogram, so the diagonals are divided in ratio 1:1.

Mid-point co-ordinates of AC= Mid-point co-ordinates of BD.

⇒

$(\frac{ - 1 + 7}{2} \: \: \frac{ - 6 + 2}{2} ) \: \: = \: ( \frac{2 + x}{2} \: \: \: \frac{ - 5 + y}{2} )$

⇒

$(3 \: \: - 2 ) = \: ( \frac{2 + x}{2} \: \: \: \frac{ - 5 + y}{2} )$

Now, comparing co-ordinates

⇒

$3 = \frac{2 + x}{2}$

⇒ 6=2+x

⇒ x=4

⇒ Now,

$- 2 = \frac{ - 5 + y}{2}$

⇒ −4=−5+y

⇒ y=1

∴ The co-ordinates of fourth vertex of parallelogram D(4,1).