Question
Question: In a triangle ABC, side AB has the equation 2x + 3y = 29 and side AC has the equation x + 2y = 16. I...
In a triangle ABC, side AB has the equation 2x + 3y = 29 and side AC has the equation x + 2y = 16. If the mid-point of BC is (5, 6) then the equation of BC is-
A
5x – 2y = 13
B
3x – 4y = – 9
C
x – y = –1
D
x + y = 11
Answer
x + y = 11
Explanation
Solution
Let D ŗ (5, 6) is mid point of BC
Equation of line through D parallel to AB meets AC at E and parallel to AC meets AB at F.
Equation to ED ŗ 2x+ 3y = 28 and equation to
FD ŗ x + 2y = 17
thus E ŗ (8, 4) and F ŗ (7, 5)
so BC is parallel to EF
Hence BC ŗ y – 6 = – 1 (x –5)
or x + y = 11