中學英數學題

15.
A (-2,-4) , B (4,5) and AP : PB = 2 : 1
x-coord of P: [2(4) + 1(-2)] / (2+1) = 2
y-coord of P: [2(5) + 1(-4)] / (2+1) = 2

16. (can't see the values)

17a.
A (2a,2a) , B (6a,-a)
AB = sqrt[(2a-6a)^2 + (2a+a)^2] = sqrt(25a^2) = 5a
17b.
C (0,7) , D (-3,3)
CD = sqrt[(0+3)^2 + (7-3)^2] = sqrt(25) = 5
AB = 3CD => 5a = 3(5) => a = 3

18a.
P (2,-1) , Q (-1,2) , R (1,-2) , S (a,b)
slope PQ: (-1-2)/(2+1) = -1
slope RS: (-2-b)/(1-a)
(-2-b)/(1-a) = -1
-2-b = -(1-a)
-2-b = -1+a
a+b = -1
18b.
T (-3,c)
equation of RS: y+2 = -1(x-1) => x + y = -1
when x = -3, y = c = 2

19a.
A (6,2) , B (8,1)
slope AB: (2-1)/(6-8) = -1/2
19b.
equation of AB: (y-2) = (-1/2)(x-6)
2(y-2) = -x + 6
x + 2y = 10
when y = 0, x = 10
19c.
slope AD: -1/slope AB = -1/(-1/2) = 2
equation of AD: y-2 = 2(x-6)
when y = 0, x = 5

20. (can't see the values)

21a.
A (-7,9) , B (-2,-1) , P (p,3)
slope AB: (9+1)/(-7+2) = -2
equation of AB: y+1 = (-2)(x+2)
2x + y = -5
when y = 3, x = -4, thus P (-4,3)
AP = sqrt[(-7+4)^2 + (9-3)^2] = sqrt(45)
PB = sqrt[(-4+2)^2 + (3+1)^2] = sqrt(20)
AP : PB = sqrt(45) : sqrt (20) = 2 : 3
21b.
p = -4 (above)

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