有無人試計依2題數...(中五)

Question 1 :
a)The coordinate of C:
Since CB//OA,
the slope of CB=the slope of OA.
Let ( 0 , a ) be the coordinates of C.
The slope of OA: 6/8 = 3/4
The slope of CB:(10-a)/(5-0)=3/4
4(10-a)=3x5
40-4a=15
a=25/4
Thus,(0,25/4)is the coordinate of C.

b)The slope of AB=(10-6)/(5-8)= (─)4/3
The slope of OA=3/4(known)
Since the slope of AB x the slope of OA=(-4/3)(3/4)=-1
AB┴OA

c)The length of OA=(6x6+8x8)←的平方根=10
...............AB=[(10-6)(10-6)+(5-8)(5-8)])←的平方根=5
...............CB=[(10-25/4)(10-25/4)+(5-0)(5-0)]←的平方根=25/4

Question 2 :
ai)Let ( c,0)be the coordinate of C.
The slope of AB=(5-4)/[3-(-1)]=1/4
The slope of BC=(5-d)/(-2)
Since AB┴BC,The slope of AB x The slope of BC= -1
(5-d)/(4 x -2) = -1
c = -3
Thus, (0,-3)is the coordinate of C.

aii)The length of AB=17的平方根
The length of BC=68的平方根
The area of triangle ABC=68的平方根x17的平方根x 1/2=17sq.units

b)Let (d,0)be the coordinate of D.
The slope of BD=5/(3-d)
The slope of AC=(-3-4)/(5+1)=-7/6
Since BD┴AC,the slope of BD x the slope of AC= -1.
7x5 = 6 (3-d)
d = -17/6