Question

If the lines $5x + 2y = 3$ and $kx + 4y = 7$ are perpendicular, what is the value of k?

• A. 8/5
• B. -8/5
• C. -2/5
• D. 2/5

Answer 1

Answer: (B)

-8/5

Answer 2

For two lines $A_1x + B_1y + C_1 = 0$ and $A_2x + B_2y + C_2 = 0$ to be perpendicular, the condition is $A_1A_2 + B_1B_2 = 0$.

Given lines are:

1. $5x + 2y = 3 \Rightarrow 5x + 2y - 3 = 0$ Here, $A_1 = 5$ and $B_1 = 2$.

2. $kx + 4y = 7 \Rightarrow kx + 4y - 7 = 0$ Here, $A_2 = k$ and $B_2 = 4$.

Applying the perpendicularity condition: $A_1A_2 + B_1B_2 = 0$ $(5)(k) + (2)(4) = 0$ $5k + 8 = 0$ $5k = -8$ $k = -\frac{8}{5}$

The value of k is $-\frac{8}{5}$.