Multiple choice general knowledge math & puzzles

Lines L1 and L2 are perpendicular that intersect at the point (2 , 3). If L1 passes through the point (0 , 2), then line L2 must pass through the point

  1. (0 , 3)

  2. (3 , 1)

  3. (6 , 7)

  4. 5 , 0)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

L1 has slope (3-2)/(2-0) = 1/2. Since L1 and L2 are perpendicular, L2's slope must be -2 (negative reciprocal). Using point-slope form through (2,3): y-3 = -2(x-2). Checking point (3,1): 1-3 = -2 and -2(3-2) = -2, so it satisfies the equation. The other options do not satisfy this line equation.

AI explanation

L1 passes through (0,2) and (2,3), giving slope = (3-2)/(2-0) = 1/2. Since L2 is perpendicular to L1 and also passes through (2,3), its slope must be the negative reciprocal: -2. The equation of L2 is y - 3 = -2(x - 2), i.e., y = -2x + 7. Testing (3,1): -2(3)+7 = -6+7 = 1, which matches — so (3,1) lies on L2, confirming it as correct. Testing the other points: (0,3) gives -2(0)+7=7≠3; (6,7) gives -2(6)+7=-5≠7; and (5,0) [likely a typo for the option] doesn't satisfy the equation either.

Keep practicing — related questions