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Question
In the given diagram, OA = OB, ∠OAB = ๐ and the line AB passes through point P (-3, 4).
Find:
- Slope and inclination (๐) of the line AB
- Equation of the line AB
Solution
OA = OB
Given, Isosceles Δ so, ∠BAO = ∠ABO = x (let)
∠BAO + ∠ABO + ∠AOB = 180° ...(โต sum of three angles of a triangle is 180°)
⇒ x + x + 90° = 180°
⇒ 2x = 90°
⇒ x = 45°
∴ ∠BAO = 45° = ๐
(a) Slope of AB = tan 45° = 1
Inclination (๐) = 45°
(b) AB has slope = 1 and passes through P (-3, 4)
∴ Equation of the line AB is
⇒ y - y1 = m(x - x1)
⇒ y - 4 = 1(x + 3)
⇒ y = x + 3 + 4
y = x + 7
⇒ x - y + 7 = 0
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