What's the idea of solving the equation of a straight line with respect to symmetry What is the train of thought? It seems that there is a step I don't understand later, that is, how can the expression of the midpoint formula be on a known line? The equation of the line 3x + 2y-2 = 0 with respect to the point (- 4,4) symmetry?

What's the idea of solving the equation of a straight line with respect to symmetry What is the train of thought? It seems that there is a step I don't understand later, that is, how can the expression of the midpoint formula be on a known line? The equation of the line 3x + 2y-2 = 0 with respect to the point (- 4,4) symmetry?

Let any point on a symmetric line be (x, y). The point of symmetry about point (- 4,4) is (x ', y')
So (x + X ') / 2 = - 4, (y + y') / 2 = 4
The solution is x '=?, y' =?
Since the point (x ', y') is on the straight line 3x + 2y-2 = 0, it is OK to find the equation of the straight line by substituting it!

When a straight line passes a point (- 2.3), when the area of the triangle formed by the straight line and the number axis is the largest, the equation of the straight line is obtained
I use parallel to make it 3x-2y + 12 = 0, which is an expert to see,

Let's define the point (- 2,3) as point a, the intersection of the line and the X axis as point B, and the intersection of the line and the Y axis as point C. because the isosceles triangle has the largest area, the triangle BOC is an isosceles right triangle. Now, let's make a vertical line ad between the point (- 2,3) and the X axis, and the length of ad is equal to the length of BD

Fifth grade equation problem, can also use equation, column vertical can also, but please write out the process, had better have ideas!
Qunfeng farm has two high producing areas of cotton. The first harvest is 1645 kg, 27.5 kg less than 1.5 times of the second harvest. How many kg of cotton can be harvested in the second high-yield field?

"Bi" exchange =, "Shao" exchange--
equation
1645=1.5X--27.5
1.5X --27.5=1645
1.5X=1672.5
X=1115

It's better to clarify the idea)
In PE class, Xiao Gang and Xiao Ming roll over the same distance with two rings of different sizes. Xiao Gang turns 50 times with the big ring and Xiao Ming turns 60 times with the small ring. It is known that the circumference of the big ring is 50cm more than that of the small ring. What is the distance?
It's best to use the proportion in volume two of grade six

If the circumference of the small ring is x cm, then according to the meaning of the title, the circumference of the large ring is (x + 50) cm
The distance Xiao Gang rolled with the big iron ring was (x + 50) × 50cm
The distance Xiao Ming rolled with a small iron ring is x × 60cm
Since Xiao Gang and Xiao Ming have the same rolling distance, the equation (x + 50) × 50 = x × 60 is given
Solve the equation and get x = 250
That is, the distance is 250 × 60 cm = 15000 cm = 150 m