Find the slope of the line that is perpendicular to the line passing through the points (-2, 3) and (2, 0). Give the perpendicular slope as an exact fraction in simplest form.

Introduction / Context:
This question tests two key coordinate-geometry ideas: (1) how to compute the slope of a line from two points, and (2) the relationship between slopes of perpendicular lines. In aptitude problems, the perpendicular slope is often found quickly by taking the negative reciprocal of the original slope, but you must compute the original slope correctly first.

Given Data / Assumptions:

• Point 1 = (-2, 3) • Point 2 = (2, 0) • Required: slope of a line perpendicular to the line through these points

Concept / Approach:
Slope between (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1). If two non-vertical lines are perpendicular, their slopes satisfy: m1 * m2 = -1. So the perpendicular slope is the negative reciprocal: m2 = -1/m1.

Step-by-Step Solution:
1) Compute the slope of the given line: m1 = (0 - 3) / (2 - (-2)) 2) Simplify the numerator and denominator: m1 = (-3) / 4 = -3/4 3) Use the perpendicular slope rule: m2 = -1/m1 4) Substitute m1 = -3/4: m2 = -1 / (-3/4) = 4/3 5) Therefore, the perpendicular slope is 4/3.

Verification / Alternative check:
Check product of slopes: (-3/4) * (4/3) = -1. Since the product is -1, the lines are perpendicular, confirming the result.

Why Other Options Are Wrong:
• -3/4 is the original slope, not the perpendicular slope. • 3/4 is the reciprocal but misses the sign change. • -4/3 has the wrong sign for perpendicularity here. • 1/4 is unrelated to the negative reciprocal rule.

Common Pitfalls:
• Forgetting the negative sign when taking the reciprocal. • Swapping the order of subtraction inconsistently (both numerator and denominator must match the same point order).

Final Answer:
4/3