Question

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocentre is at the origin, then its third vertex lies in which quadrant?

विकल्प

• third

• second

• first

• fourth

Answer 1

Second

Explanation:

Let ΔPQR with orthocentre H

Let vertex R = (x, y)

Slopes; m_QR × m_PH = –1

⇒ m_QR = `- 1/m_(PH)`

⇒ m_QR = `(y - 3)/(x - 4)` = 0

⇒ y = 3

m_PQ × m_RH = –1

⇒ `1/4 xx y/x` = –1

⇒ y = –4x

⇒ x = `-3/4`

Vertex R is `((-3)/4, 3)`

Hence, vertex R lies in second quadrant.