Coordinate Geometry
Distance Formula, Midpoint, Equation of Line
jee_main_2026_april_4_shift_2
Grade 12
Question:
The distance between the points (2, 3) and (5, 7) is d. If the midpoint of these points lies on the line 3x - 4y + k = 0, find k - d.
A. -5/2
B. -1/2
C. 9/2
D. 11/2
Step-by-Step Solution
Key Concept: Find distance using formula, then midpoint, then substitute into line equation.
Step 1: Distance d = √((5-2)^2 + (7-3)^2) = √(9+16) = 5. Step 2: Midpoint M = ((2+5)/2, (3+7)/2) = (7/2, 5). Step 3: M lies on 3x - 4y + k = 0 => 3(7/2) - 4(5) + k = 0 => 21/2 - 20 + k = 0 => 21/2 - 40/2 + k = 0 => -19/2 + k = 0 => k = 19/2. Step 4: k - d = 19/2 - 5 = 19/2 - 10/2 = 9/2.
Correct Answer: C
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