英文數學工課:Coordinate Geometry總共4頁

1.5x + 2y - 10 = 0
When y = 0; 5x = 10; x=2
Point A is (2,0)

When x=0; 2y=10; y=5
Point B is (0,5)

AB^2 = (2-0)^2+(0-5)^2
AB = square root(29)

2. A(5,2)
y = mx + c

since the line with non-zero equal intercept. slope = -1
y = -x + c
It pass through (5,2)
2=-5+c
c=7
y=-x+7
equation of straight line : x+y-7=0

3. L2 : x+y-6=0 ; slope of L2 = -1
L1 : 5x-3y-10=0 ; slope of L1 = 5/3

tanθ = (tanα - tanβ)/(1+tanαtanβ) where tanα=-1 and tanβ=5/3
tanθ = (-1-5/3)/[1+(-1)(5/3)] = (-8/3)/(-2/3)=4
θ = 76 degree
4. Solve for point A:
put x=5 into L1 : 4(5)-3y-8=0; 20-3y-8=0; 12-3y=0; y=4
Point A is (5,4)

Solve for point B:
put y=0 into L1 : 4x-8=0; x=2
Point B is (2,0)
Point C is (5,0)

Area = (1/2)(BC)(AC) = (1/2)(3)(4) = 6 square unit

5.L1 : 3x+y=0
L2 : x-3y+15=0

Prove L1 perpendicular to L2
slope of L1 : y=mx+c; y=-3x; slope=-3

slope of L2 : 3y=x+15; y=(1/3)x+5; slope=1/3

slope of L1 X slope of L2 = (-3)(1/3) = -1.
therefore L1 perpendicular to L2

Do the rest three by yourself.

6. y=mx+c

i)
c = mw + k [where c is cost; w is weight and k is a constant]

ii)when w=10 c=150; 150=10m+k
when w=18 c=214; 214=18m+k
solve m and k and then put w=25 into it.

iii)put c=195 into c = mw + k