Coordinate Geometry/Linear Equations Perpendicular/Parallel Sloes

GRE Quant Problem Solving
1

I understand the explanation behind this, however, I said D for the following reason. If L1 was a vertical line (slope of infinity), then L3 would be a horizontal line (slope of 0). M1 * M3 would be undefined (infinity * 0). Can somebody help me understand why this is always C?

Thank you.

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2

Such a line is parallel to the y-axis, which is not permitted for this question (see the second paragraph).

3

Wow… totally missed that. Thank you!