Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are $(0, - 1), (2, 1)$ and $(0, 3)$ .

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Solution

Mid Points of the sides of the triangle with the given vertices can be calculated using mid point formula
which is $(1, 0), (1, 2), (0, 1)$
Area $= 1 / 2 * [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]$
$= 1 / 2 * [0 (1 - 3) + 2 (3 + 1) + 0 (- 1 - 1)]$
$= 4 s q . u n i t s$

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Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are (0,−1),(2,1) and (0,3).

Mid Points of the sides of the triangle with the given vertices can be calculated using mid point formulawhich is (1,0),(1,2),(0,1)Area =1/2∗[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]=1/2∗[0(1−3)+2(3+1)+0(−1−1)]=4sq.units

Find the area of the triangle formed by joining the midpoints of the sides of a triangle whose vertices are $(0, - 1), (2, 1)$ and $(0, 3)$ .