Thread: Perpendicular Bisector and Circumference help

1)Show that ABC is a right-angled triangle.
2)The line y= 2x -6 is the equation of the perpendicular bisector of AC. Find the equations of the other two perpendicular bisectors of the sides of the triangle.
3)Find the circumcentre of the triangle, the point where the perpendicular bisectors intersect.
4)Write down the equation of the circle which has all three vertices of the triangle on the circumference.
5)Find the shortest distance between the line y=2x-6 and the line y=2x-1.
6)Find the length of the line y=2x-1 inside the circle.

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Thank you!

This looks like a homework exercise!

You need to remember several things:

1. Distance formula
2. How to find the midpoint/gradients of perpendicular lines
3. How to find where lines intersect
4. Think about how you might find the centre, and the radius. This is all you need
5. Draw a diagram perhaps. Shortest distances tend to be perpendicular
6. Find the intersections. Distance formula.

These should all be in your notes.

Good luck! Post back if you're struggling

Thank you so much, but what I really need is just answers with the working!