Find the answer to the last question in the final exam of mathematics in the second day of junior high school this semester (Dongcheng)

Solution: (1) Because a (-3,4), ao = √ ((-3) 2+4 2) = 5.

Because the quadrilateral ABCO is a diamond, OC=AO=5, that is, C (5,0).

Let a straight line AC: y = kx+b, then 4=-3k+b and 0 = 5k+b.

Simultaneous two formulas: k=- 1/2 and b=5/2.

So the functional relationship of AC is y=(- 1/2)x+(5/2).

(2) from ( 1): M(0，5/2)，MH=4-(5/2)=(3/2)，

It can also be seen from the figure that when P moves on AB, t=5/2 when P moves to B..

Therefore, when 0 ≤ t < 5/2 (because S≠0, t cannot be taken as 5/2), S = BP * hm = (5-2t) * (3/2) = (15/2)-3t.

When P moves on BC, T = 5； when P moves to C; According to Pythagorean theorem, MC = √ Mo 2+OC 2 = (5/2) √ 5.

AC=√(8^2+4^2)=4√5

Because AC*BO=HO*OC and BO=√5, where BD is perpendicular to AC in D and MQ is perpendicular to BC in Q on the extension line of BC.

Then BD=BO/2=(√5)/2.

Because MC*BD=BC*MQ, MQ=5/4.

So when 5/2 < t ≤ 5, S = BP * MQ = (2t-5) * (5/4) = (5/2) * t-(25/4).

So (15/2)-3t, 0 ≤ t < 5/2.

S=？

(5/2)*t-(25/4)，5/2