Question
Question: If one of the diagonals of a square is along the line x = 2y and one of its vertices is (3, 0), then...
If one of the diagonals of a square is along the line x = 2y and one of its vertices is (3, 0), then its sides through this vertex are given by the equations-
A
y –3x + 9 = 0, 3y + x – 3 = 0
B
y + 3x + 9 = 0, 3y + x –3 = 0
C
y –3x + 9 = 0, 3y – x + 3 = 0
D
y –3x + 3 = 0, 3y + x + 9 = 0
Answer
y –3x + 9 = 0, 3y + x – 3 = 0
Explanation
Solution
Clearly the point (3, 0) does not lie on the diagonal x = 2y. Let m be the slope of a side passing through (3, 0). Then its equation is y – 0 = m (x –3)… (i) since the angle between a diagonal and a side of a square is p/4. Therefore angle between x = 2y and y – 0 = m(x – 3) is also p/4, so
m = 3, –1/3.