Drawing with ruler and gauge: how to draw the parallel line of this straight line through a point outside the straight line in junior middle school?

Oh, it's a ruler and a compass
You can take a point as the center of a circle, make a circle that can intersect on a straight line, connect the two intersection points with the center of the circle, and then make an equilateral triangle. Do you know how to make the center line of the equilateral triangle, and then make the vertical line of the center line is very simple

How to draw with Geometer's Sketchpad I want to use the Geometer's Sketchpad to draw (x ^ 2-y ^ 2) (y ^ 2 + 1) = 0 But only x can't find y

The Geometer's Sketchpad doesn't seem to be able to draw images of implicit functions
If you just draw this equation, you can change it

Function image transformation order When drawing a function image, for example, the exponential function, f (x) = 2 ^| x + 1 | - 3 (- 3 is not in the index, but outside). How is the image of this function obtained by translating the image with F (x) = 2 ^ x? Do you first shift 1 unit length to the left, then 3 units down, and then turn to the left of Y axis, or Anyway, I can't figure out this kind of problem. What is the transformation order of the image with absolute value? What's more, why are exponential and logarithmic functions symmetric with respect to y = x? Can it be proved, rather than observed? What's more, the absolute value remains above the X / Y axis Image of

When there is an absolute value, the other absolute value is equal to O. if x is solved, that value is a dividing line. Just find the left and right images
The order of transformation: exponent → product → sum and difference
Why are exponential and logarithmic functions symmetric with respect to y = x?
I don't know if you've also learned about inverse functions? These two are inverse functions, and they are both symmetric about y = X
The last question is about the first one. If the absolute value is added, half of them will not change. Let's see for yourself

Some common conclusions of function image transformation

Please remember the following 7 kinds, enough to deal with all the function transformation problems in high school: (let's set a > 0) f (x) to f (x) + A: move up a unit f (x) to f (x): shift a unit to the right f (x) to AF (x): the abscissa remains unchanged, and the ordinate becomes a times of the original (a > 1) f (x) to | f (x) |: draw the image of F (x)

How to color the paintings in the Geometer's Sketchpad How to fill the color of an image

Inside the polygon step 1 select the polygon vertex 2 construction / inside the circle step 1 draw a circle 2 select the circle 3 construct / inside the circle arch (inside the sector) method step 1 draw a circle 2 draw two points on the circle 3 select two points and circle 4 "construct / arc on circle" 5 select arc 6 "construct"

Draw curves on the Geometer's Sketchpad. Irregular curves, general curve equations Irregular curve, general curve equation, such as x ^ 2 + y ^ 3 + X * y = 5 image? This is not a function, so I don't know how to draw

You're right. How can an X have two Y values? Just think about the definition of function. The Geometer's Sketchpad draws functions, not all equations. Functions have a certain y, two equations for every x, and sometimes there are more than two Y corresponding for an X

Drawing parametric equation curves with Geometer's Sketchpad Can the Geometer's Sketchpad draw curves of parametric equations? For example, the parameter equation x = 2cos (T); y = 3sin (T) Can you draw curves with the Geometer's Sketchpad? The key is how to operate! And now the parametric equation of the curve to be drawn can hardly eliminate parameters

There are many methods
Go, I'll just say one
Create a new parameter t first
Then use "data" to "calculate":
2cos (T) and y = 3sin (T)
Reuse
”Drawing points
then
Click "Edit" operation button "animation
Set t from - 180 to 180
Finally, trace is used to draw points
Then click the animation parameters button
It's done~

Drawing parametric curves with Geometer's Sketchpad How to use the Geometer's Sketchpad to draw a curve with parameters? (that is, there is a parameter in the analytic formula of the function. The point representing the parameter can be placed on a straight line. Drag the point to change the parameter value and see the corresponding function image.)

First construct a parameter and use it in the input function

How to draw the intersection of two functions and two curves in the Geometer's Sketchpad

If your function image is obtained by drawing a function, then their intersection point can be placed near the intersection point. If two curves are constructed by trajectories, it seems that there is no such function to construct their intersection point so far, it is recommended to use the first floor method

How does the Geometer's Sketchpad draw y ^ 2 = x ^ 2

Because this is not a function, it can't be expressed directly. It can be drawn only by dissolving it. You can know that y = x or y = - x in the Geometer's Sketchpad. As long as the images of y = x and y = - X are drawn, these two lines are the images of Y? = x

Drawing with ruler and gauge: how to draw the parallel line of this straight line through a point outside the straight line in junior middle school?