Question

if (1,2) (4,y) (x,6) and (3,5)are vertices of parrallgram. find x and y​

Answer 1

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In ||gm diagonals Bisect each other

Suppose

A(1,2) = A(x1, y1)

B(4,y) = B(x2, y2)

C(x,6) = C(x3, y3)

D(3,5) = D(x4, y4)

Let the Midpoint of diagonal Be P(a, b)

Midpoint of AC is P

• $a= \frac{x1 + x3}{2}$
• $a = \frac{x + 1}{2}$
• $b = \frac{y1 + y3}{2}$
• $b = \frac{7}{2}$

Midpoint of BD is P

• $a = \frac{x2 + x4}{2}$
• $a = \frac{7}{2}$
• $b = \frac{y2 + y4}{2}$
• $b = \frac{y + 5}{2}$

Comparing both we get

• $\frac{x + 1}{2} = \frac{7}{2}$
• $x = 6$
• $\frac{y + 5}{2} = \frac{7}{2}$
• $y = 2$
• Therefore X = 6 and Y = 2