حل السؤال 25، 4MA1/2HR يونيو 2023: المنصف العمودي

1. 1y − 2x = 7 rearranges to y = 2x + 7, so the bisector has gradient 2
2. 2AB is perpendicular to the bisector, so AB has gradient −1/2
3. 3Gradient of AB = (k − 7)/(6 − j) = −1/2, so 2k − 14 = j − 6 and j = 2k − 8
4. 4The midpoint ((j + 6)/2, (7 + k)/2) lies on the bisector
5. 5So (7 + k)/2 = 2 × (j + 6)/2 + 7, which gives 7 + k = 2j + 26 and k = 2j + 19
6. 6Substitute j = 2k − 8: k = 2(2k − 8) + 19 = 4k + 3, so 3k = −3 and k = −1
7. 7Then j = 2 × (−1) − 8 = −10
8. 8Midpoint = ((−10 + 6)/2, (7 + (−1))/2) = (−2, 3)

Answer(−2, 3)