The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). F

1.	The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.
Answer» Consider A(3, 4), B (3, 8) and C(9, 8). Let the coordinates of fourth vertex are D (x, y) In a parallelogram diagonals bisect each other Coordinate of mid point of AC = X = \(\frac{3 + 9}2\) = \(\frac{12}2\) = 6 Y = \(\frac{4 + 8}2\) = \(\frac{12}2\) = 6 Therefore coordinates of mid point of AC are (6, 6) Coordinate of mid point of BD = X = \(\frac{3 + x}2\) Y = \(\frac{y + 8}2\) Coordinates of point D are \(\frac{3 + x}2\) = 6 x = 12 - 3 = 9 \(\frac{y + 8}2\) = 6 y = 12 - 8 = 4 Therefore coordinates of fourth vertex D are (9, 4)

The three vertices of a parallelogram are (3, 4), (3, 8) and (9, 8). Find the fourth vertex.

Answer»

Consider A(3, 4), B (3, 8) and C(9, 8).

Let the coordinates of fourth vertex are D (x, y)

In a parallelogram diagonals bisect each other

Coordinate of mid point of AC = X = \(\frac{3 + 9}2\) = \(\frac{12}2\) = 6

Y = \(\frac{4 + 8}2\) = \(\frac{12}2\) = 6

Therefore coordinates of mid point of AC are (6, 6) Coordinate of mid point of BD = X = \(\frac{3 + x}2\)

Y = \(\frac{y + 8}2\)

Coordinates of point D are

\(\frac{3 + x}2\) = 6

x = 12 - 3 = 9

\(\frac{y + 8}2\) = 6

y = 12 - 8 = 4

Therefore coordinates of fourth vertex D are (9, 4)

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