OCR PURE — Question 6

Exam BoardOCR
ModulePURE
TopicCircles

6 The vertices of triangle \(A B C\) are \(A ( - 3,1 ) , B ( 5,0 )\) and \(C ( 9,7 )\).
  1. Show that \(A B = B C\).
  2. Show that angle \(A B C\) is not a right angle.
  3. Find the coordinates of the midpoint of \(A C\).
  4. Determine the equation of the line of symmetry of the triangle, giving your answer in the form \(p x + q y = r\), where \(p , q\) and \(r\) are integers to be determined.
  5. Write down an equation of the circle with centre \(A\) which passes through \(B\). This circle intersects the line of symmetry of the triangle at \(B\) and at a second point.
  6. Find the coordinates of this second point.