# Answer the following question: The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of altitudes of ∆ABC - Mathematics and Statistics

Sum

The vertices of a triangle are A(1, 4), B(2, 3) and C(1, 6) Find equations of altitudes of ∆ABC

#### Solution

Let AX, BY and CZ be the altitudes through the vertices A, B and C respectively of ∆ABC.

Slope of BC = – 3

∴ Slope of AX = 1/3   ...[∵ AX ⊥ BC]

Since altitude AX passes through (1, 4) and has slope 1/3,
equation of altitude AX is

y – 4 = 1/3(x - 1)

∴ 3y – 12 = x – 1

∴ x – 3y + 11 = 0

Since both the points A and C have same x co-ordinates i.e. 1,

the points A and C lie on the line x = 1.

AC is parallel to Y-axis and therefore, altitude

BY is parallel to X-axis

Since the altitude BY passes through B(2, 3),

the equation of altitude BY is y = 3.

Also, slope of AB = – 1

∴ Slope of CZ = 1

Since altitude CZ passes through (1, 6) and has slope 1,

equation of altitude CZ is

y – 6 = 1(x – 1)

∴ x – y + 5 = 0

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board
Chapter 5 Straight Line
Miscellaneous Exercise 5 | Q II. (13) (d) | Page 125