In Figure, the vertices of Δ ABC are A(4, 6), B(1, 5) and C(7, 2). A line segment DE is drawn to intersect the sides AB and AC at D and E respectively such that

Calculate the area of Δ ADE and compare it with an area of Δ ABC.

The points A (4, 7), B (p, 3) and C (7, 3) are the vertices a right triangle, right-angled at B find the value of p.

Find the relation between x and y if the points A (x, y), B (-5, 7) and C (-4, 5) are collinear.

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP = 3/7 AB, where P lies on the line segment AB.

375. The diagonal of a rectangular field is 16 metres more than the shorter side. If the longer side is 14 metres more than the shorter side, then find the lengths of the sides of the field.

Find the values of k so that the area of the triangle with vertices (1,-1), (-4, 2k) and (-k, 5) is 24 sq. units

If the distance between the points (4, k) and (1, 0) is 5, then what can be the possible values of k?

The area of a triangle is 5 sq units. Two of its vertices are (2, 1) and (3, –2). If the third vertex is (7/2, y), find the value of y.

If a≠b≠0, prove that the points (a, a2), (b, b2) (0, 0) will not be collinear.