3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
A
-\(\frac{4}{3}\)
B
-\(\frac{3}{4}\)
C
\(\frac{3}{4}\)
D
\(\frac{4}{3}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
Grad of 3y = 4x - 1
y = \(\frac{4x}{3}\) - \(\frac{1}{3}\)
Grad = \(\frac{4}{3}\)
Grad of Ky = x + 3
y = \(\frac{\text{x}}{\text{k}}\) + \(\frac{3}{4}\)
Grad = \(\frac{1}{\text{k}}\)
Since the two lines are perpendicular,
\(\frac{1}{\text{k}}\) = -\(\frac{3}{4}\)
-3k = 4
k = -\(\frac{4}{3}\)
Source: Myschool Past Questions Archive (Record #792)