Ques 3 Find the coordinates of the point which is equidistant from the vertices of a ABC, where A (3, -1), B (-1, -6) and C (4, -1).

To find the coordinates of the point which is equidistant from the vertices of a triangle ABC, we need to find the coordinates of the circumcenter of the triangle. The circumcenter of a triangle is the point where the perpendicular bisectors of the sides intersect, and it is equidistant from the vertices of the triangle.

Here are the steps to find the circumcenter:

1. Find the midpoint of AB: Midpoint formula = ((x1 + x2)/2, (y1 + y2)/2) Midpoint D of AB = ((3 - 1)/2, (-1 - 6)/2) = (1, -3.5)

2. Find the slope of AB: Slope formula = (y2 - y1) / (x2 - x1) Slope of AB = ((-6 - (-1)) / (-1 - 3)) = 5/4

3. Find the slope of the perpendicular bisector of AB: The slope of the perpendicular line = -1 / slope of the line Slope of the perpendicular bisector of AB = -1 / (5/4) = -4/5

4. Find the equation of the line passing through D and having the slope -4/5: Equation of the line formula: y - y1 = m(x - x1) Equation of the line = y + 3.5 = -4/5(x - 1)

5. Repeat steps 1-4 for the line BC.

6. Solve the two equations obtained in steps 4 and 5 to find the coordinates of the circumcenter.

Note: This is a general method to find the circumcenter of a triangle. In some cases, it might be easier to use other properties of the circumcenter. For example, in an equilateral triangle, the circumcenter is also the centroid and the incenter of the triangle.