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Mathematics for entrance examination of senior one.
1 BC slope = (1-2)/(9-7) =-1/2.

AD slope =(y- 1)/(x- 1)

AD//BC, then (y-1)/(x-1) =-1/2.

2y+x-3=0

(2)

AC slope =0, BD slope =((y-2)/(x-7).

AC⊥BD must be x=7.

Bring 1

2y+7-3=0

y=-2

In a word, x = 7 and y =-2.

Vector BC={2,-1}, CD={-2, -3}

|BC|= root number 5, |CD|= root number 13.

BC. CD = 2×(-2)+(- 1)×(-3)=- 1

Bc, cosine of CD angle = BC, CD/| BC | | CD | =- 1/ root sign (65)