ConceptArea of a Triangle

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#### Question

Find the area of the triangle ABC with A(1, −4) and mid-points of sides through A being (2, −1) and (0, −1).

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median of a triangle divides it into two triangles of equal areas. Verify this result for ΔABC whose vertices are A (4, - 6), B (3, - 2) and C (5, 2).

If A(−4, 8), B(−3, −4), C(0, −5) and D(5, 6) are the vertices of a quadrilateral ABCD, find its area.

If the points A(−1, −4), B(*b*, *c*) and C(5, −1) are collinear and 2*b* + *c* = 4, find the values of *b* and *c*.

For what value of x will the points (x, –1), (2, 1) and (4, 5) lie on a line ?

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

#### Reference Material

Solution for concept: Area of a Triangle. For the course 8th-10th CBSE