(2,1)
Translating a point 4 units to the right means adding 4 to the x-coordinate, and translating it 5 units down means subtracting 5 from the y-coordinate. So, if the original point is (x, y), the new point after the translation would be (x+4, y-5). This transformation is a type of rigid transformation known as a translation, which moves the entire figure without changing its size or shape.
Not sure
The new coordinates are(3 + the old 'x', 2 + the old 'y')
For a start, you would need an initial equation. A horizontal translation of ANY equation can be achieved by replacing every ocurrence of "x" with "x - a", where "a" is the amount you want to move the graph to the right. For example, replacing every ocurrence of "x" by "x - 10" will move your graph 10 units to the right.
the number 2 is two units to the right of 0 on the number line. the number -2 is two units to the left of 0
If you we're at the point (8,-2) and you went 5 units right and 2 units up, you'd be at (13,0).
The coordinates are (10, 5).
Here's an example: In the coordinate plane, the point is translated to the point . Under the same translation, the points and are translated to and , respectively. What are the coordinates of and ? Any translation sends a point to a point . For the point in the problem, we have the following. So we have . Solving for and , we get and . So the translation is unit to the right and units up. See Figure 1. We can now find and . They come from the same translation: unit to the right and units up. The three points and their translations are shown in Figure 2.
A translation of 4 units to the right followed by a dilation of a factor of 2
(z,z+2) or (z+2,z)
the translation of 2 is the one that triangle moves by 4 units right and 8 units up
A reflection across the origin transforms a point ((x, y)) to ((-x, -y)). After this reflection, a translation of 3 units to the right and 4 units up shifts the point to ((-x + 3, -y + 4)). Therefore, the combined rule for the transformation is given by the mapping ((x, y) \to (-x + 3, -y + 4)).
A function that translates a point ((x, y)) to the right by (a) units and up by (b) units can be expressed as (f(x, y) = (x + a, y + b)). This means you simply add (a) to the x-coordinate and (b) to the y-coordinate of the original point. In function notation, if (f(x, y)) represents the original point, the translated point can be represented as (f'(x, y) = (x + a, y + b)).
They are (a, b-4).
(x,y) > (x + 8, y + 2)
The coordinates of a point two units to the right of the y-axis and three units above the x-axis would be (2,3).
For this translation, you need to replace every occurence of "x" with "x-3", and every occurence of "y" with "y+5".