The coordinates of the points A, B and C are (−2, 3), (1, 1) and (1, 4) respectively. Find the
equation of the perpendicular from the point B to the line AC and the coordinates of the
foot of that perpendicular.
The coordinates of the points A, B and C are A(−2, 3), B(1, 1) and
C (1, 4) .
equation of line AC
slope of line AC=1/3
Let BM be the perpendicular from B on to AC.
product of slopes of AC and BM =-1
Thus slope of lineBM=-3
Thus equation of line BM is
The point of intersection of (i) and (ii) are
is the coordinate of foot of perpendicular from B to AC.
solving above equations ,we have
Thus coordinate of `M(1/10,37/8)`
We have used formula for line AC is