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Mathematics high school examination questions
Solution: 1 Let M(x0, y0) be the midpoint of AB:

From the midpoint coordinate formula:

x0=(2+0)/2= 1,y0=(4+(-2))/2= 1

M( 1, 1)? .

Let the equation of the straight line where the center line CM of AB side is located be:

y=kx+b,

Substitute c (-2,3) and M( 1, 1),

Solve the equation:

3=-2k+b? ( 1)?

1=k+b? (2)

Get k=-2/3.

b=5/3

∴ The equation of the straight line where the center line CM of AB side is located is:

y? =? -? 2x/3? +? 5/3。

2.? In the same way.

The equation of straight line with AB edge is:

y-4=3(x-2)

3x-y-2=0。

Distance from point C (-2,3) to straight line AB: 3x-y-2 = 0.

d = | 3 *(2)-3-2 |/√? 10

= 1 1√? 10/ 10.

Get S△ABC=|AB|*d/2.

=2√ 10*( 1 1√? 10/ 10)/2

= 1 1.