An isosceles triangle abc where ab=bc. the line bd is perpendicular to the line ac. given that the gradient of line ac=-2/3.find coordinate of point a

To find the coordinate of A you can first determine the coordinate of D and apply the midpoint rule.

And to find the coordinates of D you must solve equations of AC and BD simultaneously.

AC has equation



Or



BD has equation



Or



Multiply equation (1) by 2 and multiply equation (2) by 3 to obtain,





Equation (3) minus equation (4)

gives




Putting the value of x=4 in equation (4) gives



This implies that








Solving the equations of AC and BD simultaneously give the coordinates of D to be;



Let

be the coordinates.

Since D is the midpoint of AC



and



Solving for m and n, we have



And



Therefore A has coordinates

[tex] (-2,8)/tex]