حل السؤال 24، 4024/12 مايو/يونيو 2023: المنصف العمودي

1. 1Midpoint of AB = ((3 + (−5))/2, (11 + (−5))/2) = (−1, 3)
2. 2Gradient of AB = (11 − (−5))/(3 − (−5)) = 16/8 = 2
3. 3L: 2y = −x + 5, so y = −1/2 x + 5/2, gradient −1/2
4. 42 × (−1/2) = −1, so L is perpendicular to AB
5. 5At (−1, 3): 2 × 3 + (−1) = 5, so the midpoint (−1, 3) lies on L
6. 6So L is the perpendicular bisector of AB

AnswerMidpoint of AB = (−1, 3); gradient of AB = 2, so gradient of perpendicular = −1/2; 2 × 3 + −1 = 5 so (−1, 3) is on L, and gradient of L = −1/(gradient AB)