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Q: How can the movement of a figure either up or right on a coordinate grir both be considered translations?

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Neither, as a graph can be read from either axis to get a value on the other axis. However, the y coordinate is usually considered the dependent variable as an equation is usually written as y = f(x), so it could be considered the output.

the first coordinate goes on the X axis, either positive (To the right of the Y axis) or negative (to the left of the Y axis). The second coordinate goes on the Y axis, either positive (above the X axis) or negative (below the X axis).

The word abscissa can either refer the horizontal axis (the x-axis) in a cartesian coordinate system or the actual coordinate plotted on the horizontal axis.

In the context of a circle or the coordinate plane, quadrants are the four quarters defined either by two mutually perpendicular radii or the coordinate axes.

It could have been either but it must have been easier to put the y-coordinate on top.

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Transformations can be Translations--slide Reflections--flip Rotation--turn Dilation--either bigger or smaller

Neither, as a graph can be read from either axis to get a value on the other axis. However, the y coordinate is usually considered the dependent variable as an equation is usually written as y = f(x), so it could be considered the output.

it is called the Cartesian Coordinate Plane

Traslation comes from the Latin root meaning to "move across". The movement of a figure up (or down) or right (or left) are rightly considered translation.

No, "either" is not a preposition. It is either used as a coordinate conjunction or a determiner.

the first coordinate goes on the X axis, either positive (To the right of the Y axis) or negative (to the left of the Y axis). The second coordinate goes on the Y axis, either positive (above the X axis) or negative (below the X axis).

Neither.

The word abscissa can either refer the horizontal axis (the x-axis) in a cartesian coordinate system or the actual coordinate plotted on the horizontal axis.

In the context of a circle or the coordinate plane, quadrants are the four quarters defined either by two mutually perpendicular radii or the coordinate axes.

You could rotate it in either direction, like a steering wheel. -- If you rotate the whole plane 90 degrees to the left, then the old x-coordinate of every point becomes its new y-coordinate, and its old y-coordinate becomes its negative x-coordinate. -- If you rotate the whole plane 90 degrees to the right, then the old x-coordinate of every point becomes its new negative y-coordinate, and its old y-coordinate becomes its new x-coordinate.

To find out the coordinates of a point in the coordinate system you do the opposite. Begin at the point and follow a vertical line either up or down to the x-axis. There is your x-coordinate. And then do the same but following a horizontal line to find the y-coordinate.

I think the word that you're looking for is coordinate. that can either mean a coordinate, like, a plot on a graph (co-ordinet) or coordinate, to align or order something, to allocate positions in a team, something like that (co-ordinate) Hope this helps... =)