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 \(D\) \(=\) $\left(i,i\right)$