Question

Given A (6, 3),  B (– 3, 5) and C (4, – 2) are the vertices of ∆ ABC.

1. Write the equations of the sides of the triangle. 
2. Write the equations of the perpendicular bisectors of the sides of the triangle. 
3. Write the equations of all its medians and altitudes. 
4. Find the points of intersection of all the pairs of medians. 
5. Find the points of intersection of all the pairs of altitudes.   
6. Find the points of intersection of all the pairs of perpendicular bisectors of the sides of the triangle. 
7. Are the medians of the triangle concurrent? Explain?
8. Are the altitudes of the triangle concurrent? Explain?
9. Are the perpendicular bisectors of the sides of the triangle concurrent? Explain? 
10. Find the lengths of all the medians and altitudes.
11. Consider a line mirror along the line BC and find the reflection of the vertex A about line BC.