The mid-point of the line segment joining the points $P(-4,5)$ and $Q(4,6)$ lies on:
[1]
The coordinates of the centre of a circle are $(2a,a-7)$. Find the value(s) of 'a' if the circle passes through the point $(11,-9)$ and has diameter $10\sqrt{2}$ units.
[2]
Find the ratio in which the y-axis divides the line segment joining the points $(5,6)$ and $(-1,-4)$. Also find the point of intersection.
[3]
AD is a median of $\Delta ABC$ with vertices $A(5,-6)$, $B(6,4)$ and $C(0,0)$. Length AD is equal to:
[1 mark]
If the distance between the points $(3,-5)$ and $(x,-5)$ is 15 units, then the values of x are:
[1 mark]
The centre of a circle is at (2, 0). If one end of a diameter is at (6, 0), then the other end is at :
[1 mark]
Find the ratio in which the point $(\frac{8}{5},y)$ divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y.
[3 marks]
ABCD is a rectangle formed by the points $A(-1,-1)$, B (-1, 6), C (3, 6) and D (3, -1). P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other.
[3 marks]
In what ratio, does x-axis divide the line segment joining the points \( A(3,6) \) and \( B(-12,-3) \)?
[1 mark]
The distance between the points \( (0, 2\sqrt{5}) \) and \( (-2\sqrt{5}, 0) \) is
[1 mark]
If (-5, 3) and (5, 3) are two vertices of an equilateral triangle, then find co-ordinates of the third vertex, given that origin lies inside the triangle. (Take \( \sqrt{3}=1.7 \))
[3 marks]