If the point C(-1, 2) divides internally the line-segment joining the points A(2, 5) and B(x,y) in the ratio 3 : 4, find the value of  x² + y².

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

Question 21.
For what values of k are the points (8,1), (3, -2k) and (k, -5) collinear?

Find the coordinates of a point P on the line segment joining A(1, 2) and B(6,7) such that AP=\( \frac{2}{5} \)AB

Find the value(s) of k for which the points (3k – 1, k – 2), (k, k-1) and (k – 1, – k – 2) are collinear

If A(4,2), B(7,6) and C(l, 4) are the vertices of a ∆ABC and AD is its median, prove that the median AD divides ∆ABC into two triangles of equal areas

Prove that the points A(0, -1), B(-2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?

Prove that the points A(2, -1), B(3, 4), C(-2, 3) and D(-3, -2) are the vertices of a rhombus ABCD. Is ABCD a square?

If the point P(x,y) is equidistant from two points A (-3,2) and B (4, -5), prove that y = x- 2

Find the value of x for which the points (x – 1), (2,1) and (4,5) are collinear

If the points A(l, -2), B(2,3), C(-3,2) and D(-4, -3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of this parallelogram

For what value of k, (k > 0), is the area of the triangle with vertices (-2, 5), (k, -4) and {2k + 1,10) equal to 53 sq. units?

Find the value of k, if the points P(5,4), Q(7, k) and R(9, -2) are collinear

What is the distance between the points A(c, 0) and B(0, -c)?

Find the value of k, if the points A(7, -2), B(5,1) and C(3,2k) are collinear

If the points (p, q); (m, n) and (p-m,q-n) are collinear, show that pn = qm

Find the value of k, if the points A(8,1), B(3, -4) and C(2, k) are collinear