10. Five marks exercise problems IV

1. $O(0,0)$ is the centre of a circle whose one chord is $AB$, where the points $A$ and $B$ are $(8,6)$ and $(10,0)$ respectively. $OD$ is the perpendicular from the centre to the chord $AB$. Find the coordinates of the mid-point of $OD$.

 

The coordinates of the mid-point of $OD$ $=$ $\left(i,i\right)$

 

 

2. The points $A(−5, 4)$, $B(-1, -2)$ and $C(5, 2)$ are the vertices of an isosceles right-angled triangle where the right angle is at $B$. Find the coordinates of $D$ so that $ABCD$ is a square.

 

The coordinates of $D$ $=$ $\left(i,i\right)$