Test Index

UPSC NDA I 2015 Mathematics Paper

Question Numbers: 43-45

For the next three (3) items that follow:

Consider the triangle ABC with vertices A(-2, 3), B(2, 1) and C(1, 2).

Question : 45 of 120

Marks: +1, -0

What is the foot of the altitude from the vertex A of the triangle ABC?

Solution:

Concept:

The foot of the altitude from vertex

A

to side

BC

is the point where the perpendicular from

A

meets

BC

Explanation:

Given:

A(-2,3)

B(2,1)

C(1,2)

Slope of

BC = \frac{(2-1)}{(1-2)} = -1

Equation of

BC

(y-1) = -1(x-2) \implies x+y=3

. (1)

Since

AD \perp BC

, slope of

AD \times (-1) = -1 \implies

slope of

AD = 1

Equation of

AD

through

A(-2,3)

(y-3) = 1(x+2) \implies y - x = 5

. (2)

Solve (1) and (2): add to get

2y = 8 \implies y = 4

Substitute

y = 4

in (1):

4+x=3 \implies x = -1

Thus foot of altitude is

(-1,4)

Answer:

(-1,4)

(Option D).

Go to Question:

Prev Question

Next Question