Question

Let A = (−2, 6), B = (1, 0), and C = (5, 2). Prove that △ABC is a right-angled triangle.Let u = AB, v = BC, and w = AC. We must show that u · v, u · w, or v · w is zero in order to show that one of these pairs is orthogonal.u · v = Incorrect: Your answer is incorrect.u · w = Incorrect: Your answer is incorrect.v · w = Incorrect: Your answer is incorrect.

Answer 1

Answer:

Step-by-step explanation:

In a triangle ABC, given A= (-2,6),

B = (1,0) and C = (5,2)

If u = AB, v = BC, w = AC

To show that the triangle is a right angled triangle, we must show that the dot product of one of the pairs is zero.

Since u = AB

u = AB = B-A

u = AB = (1,0) - (-2,6)

u = [(1-(-2), 0-6]

u = (3, -6)

Similarly, v = BC = C-B

v = BC = (5,2) - (1,0)

v = [(5-1), (2-0)]

v = (4, 2)

Also for w:

w = AC = C - A

w = (5, 2) - (2, -6)

w = [(5-2), (2-(-6)]

w = (3, 8)

To show that the triangle is a right angled triangle, the dot product of one of any of the pairs must be zero as shown:

u.v = (3, -6) • (4, 2)

u.v = (3)(4) + (-6)(2)

u.v = 12-12

u.v = 0

i.e AB.BC = 0

This shows that length AB and BC are perpendicular to each other i.e the angle between them is 90° and since a right angled triangle has one of its angle to be 90°, it shows that the ∆ABC is a right angled triangle.