Moderate -0.5 This is a straightforward coordinate geometry question requiring standard techniques: showing perpendicularity via gradient product = -1, then using the right angle property to identify the hypotenuse as diameter. Both parts are routine A-level methods with no conceptual challenges, making it slightly easier than average.
The coordinates of three points \(A , B , C\) are \(( 4,6 ) , ( - 3,5 )\) and \(( 5 , - 1 )\) respectively.
a) Show that \(B \widehat { A C }\) is a right angle.
b) A circle passes through all three points \(A , B , C\). Determine the equation of the circle.
The coordinates of three points $A , B , C$ are $( 4,6 ) , ( - 3,5 )$ and $( 5 , - 1 )$ respectively.
a) Show that $B \widehat { A C }$ is a right angle.\\
b) A circle passes through all three points $A , B , C$. Determine the equation of the circle.
\hfill \mbox{\textit{WJEC Unit 1 2018 Q18}}