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.

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

377.

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.