F.3 MATHS

斜率(slope) SP = (5 – y)/(2 – x)
斜率RQ = (1 – (-2))/(5 – 1) = ¾
斜率SP =斜率RQ (SP平行RQ)
(5 – y)/(2 – x) = ¾
4 (5 – y) = 3(2-x)
20 – 4y = 6 – 3x
3x - 4y = 6 – 20
3x - 4y = -14 -------------------- (1)

斜率SR = (-2 – y)/(1 – x)
斜率PQ = (5-1)/(2 – 5) = 4/-3 = -4/3
斜率SR = 斜率PQ (SR平行 PQ)
(-2 – y)/(1 – x) = -4/3
3(-2 – y) = -4(1 – x)
-6 – 3y =-4 +4x
4x + 3y = -6 +4
4x + 3y = -2 -------------------- (2)
3x - 4y = -14 ------------------ (1)
16x + 12y = -8 等式 (2) 乘4
9x – 12y = -42 等式 (1)乘 3
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25x = -50
x = -50/25 = -2
(1a)
3x - 4y = -14
3(-2) - 4y = -14
-6 - 4y = -14
4y = -6 +14
4y = 8
y = 8/4 = 2

S的坐標 (-2, 2)