Question

Answer the following question:

A(1, 4), B(2, 3) and C(1, 6) are vertices of ∆ABC. Find the equation of the altitude through B and hence find the co-ordinates of the point where this altitude cuts the side AC of ∆ABC.

Answer 1

Vertices of the triangle are A(1, 4), B(2, 3), and C(1, 6).

Let BD be the altitude through vertex B.

Since both the points A and C have the same x co-ordinates i.e. 1, the given points lie on a line parallel to Y-axis.

∴ The equation of the line AC is x = 1 ....(i)

AC is parallel to Y-axis and therefore, altitude BD is parallel to X-axis.

Since the altitude BD passes through B(2, 3), the equation of altitude BD is y = 3 .......(ii)

From (i) and (ii),

Point of intersection of AC and altitude BD is (1, 3).