The points (–4, 0), (4, 0), (0, 3) are the vertices of a
(A) right triangle (B) isosceles triangle
(C) equilateral triangle (D) scalene triangle
Last updated at Aug. 16, 2021 by Teachoo
Transcript
Question 11 The points (–4, 0), (4, 0), (0, 3) are the vertices of a (A) right triangle (B) isosceles triangle (C) equilateral triangle (D) scalene triangle Let A (−4, 0), B (4, 0) and C (0, 3) Let’s find AB, BC and AC Finding AB AB = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √(( 4−(−4))2+(0 −0)2) = √((4+4)2+(0)2) = √(8^2+0) = √(8^2 ) = 8 units Finding AC Here, A (−4, 0) and C (0, 3) AC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((0−(−4))2+(3 −0)2) = √(42+32) = √(16+9) = √25 = √(5^2 ) = 5 units Finding BC Here, B (4, 0) and C (0, 3) BC = √((𝑥2 −𝑥1)2+(𝑦2 −𝑦1)2) = √((0−4)2+(3 −0)2) = √((−4)2+32) = √(16+9) = √25 = √(5^2 ) = 5 units Thus, AB = 8, AC = 5, BC = 5 Since AC = BC ∴ Two sides of the Δ ABC are equal Hence, Δ ABC is an isosceles triangle So, the correct answer is (B)
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