Question
Question: Let A ≡ (−2, 0), B ≡ (4, 0), C ≡ (h, h). If perimeter of triangle ABC is minimum then...
Let A ≡ (−2, 0), B ≡ (4, 0), C ≡ (h, h). If perimeter of triangle ABC is minimum then
A
h = 1
B
h = -1
C
h = 2
D
) None of these
Answer
h = -1
Explanation
Solution
B,(0, 4) is the reflection of B in y = x, we have AB + AC + BC = AB + AC + CB1. Thus for perimeter to be minimum AC + CB, must be minimum. That means light rays emerging from A(-2, 0) after getting reflected from y = x at C, must pass through B1.
Which implies C ≡ (0, 0). But in this case ∆ABC can't be formed. Thus no such point can be located.