how can you determine the coordinates of the point of intersection of a perpendicular and the corresponding base of any triangle, if the coordinates of its vertices are given?

dear student,

let us consider a triangle ABC,

where AD is the perpendicular on BC.

we can find the slope of BC using the coordinates of B and C.

now,

product of the slopes of AD and BC has to be -1....as they are perpendicular lines.

so you can find the equation of the line AD using slope point form as the coordinats of A are known.

now find the equation of BC using two point form.

solve the equations of AD and BC, to get the coordinates of D

hope this clarifies your doubt.

regards

team

topperlearning