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Find the area of the triangle formed by joining the mid–points

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Find the area of the triangle formed by joining the mid–points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

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Find the area of the triangle formed by joining the mid–points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

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Text solutionVerified

Solution:

D = ((\frac{2}{2}), \frac{1 - 1}{2}) = (1, 0)

E = ((\frac{2}{2}), \frac{1 + 3}{2}) = (1, 2)

F = (0, \frac{3 - 1}{2}) = (0, 1)

Area of

∠ D E F = \frac{1}{2} (x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2}))

\frac{1}{2} (1 (2 - 1) + 1 (1 - 0) + 0)

=1
Area of

∠ A B C = \frac{1}{2} (0 + 2 (3 + 1) + 0)

=4
ratio=

\frac{a r e a ∠ D E F}{a r e a ∠ A B C} = \frac{1}{4}

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Question Text	Find the area of the triangle formed by joining the mid–points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.
Answer Type	Text solution:1
Upvotes	150

Find the area of the triangle formed by joining the mid–points of the sides of the triangle whose vertices are (0, –1), (2, 1) and (0, 3). Find the ratio of this area to the area of the given triangle.

Text solutionVerified

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