Question

Lines \(L_1\) and \(L_2\) have slopes 2 and \(-\frac{1}{2}\) respectively. If both \(L_1\) and \(L_2\) are concurrent with the lines \(x - y + 2 = 0\) and \(2x + y + 3 = 0\), then the sum of the absolute values of the intercepts made by the lines \(L_1\) and \(L_2\) on the coordinate axes is?

• A. 2
• B. 7
• C. 12
• D. 9

Hint:

Use concurrency conditions and slope-intercept form to find intercepts and sum their absolute values.

Answer 1

The Correct Option is B

Let equations be \(L_1: y = 2x + c_1\), \(L_2: y = -\frac{1}{2}x + c_2\). Using concurrency with given lines, solve for \(c_1, c_2\). Intercepts for \(L_1\): \(x\)-intercept \(-\frac{c_1}{2}\), \(y\)-intercept \(c_1\). Intercepts for \(L_2\): \(x\)-intercept \(-2 c_2\), \(y\)-intercept \(c_2\). Sum of absolute intercepts: \[ |c_1| + \left|\frac{c_1}{2}\right| + |c_2| + |2 c_2| = 7. \]