Question

(x, y)→(x+3, y-10)

Explanation:

This is a transformation rule for a point \((x,y)\) in a coordinate plane. If we want to find the image of a given point, we substitute the \(x\) - coordinate of the original point into \(x + 3\) and the \(y\) - coordinate of the original point into \(y-10\). But since no original point is given, we can just explain the transformation.

For example, if we have a point \((x_0,y_0)\), the image of the point after the transformation \((x,y)\to(x + 3,y-10)\) will be \((x_0+3,y_0 - 10)\). This represents a translation in the coordinate plane. The \(x\) - coordinate of the point is shifted 3 units to the right (because we add 3 to \(x\)) and the \(y\) - coordinate is shifted 10 units down (because we subtract 10 from \(y\)).

If you want to apply this to a specific point, say \((2,5)\):

Step 1: Substitute \(x = 2\) into \(x+3\)

\(x+3=2 + 3=5\)

Step 2: Substitute \(y = 5\) into \(y - 10\)

\(y-10=5-10=- 5\)

So the image of the point \((2,5)\) under the transformation \((x,y)\to(x + 3,y-10)\) is \((5,-5)\)

Answer:

If we consider a general point \((x,y)\), its image is \((x + 3,y-10)\). For a specific point (e.g., \((2,5)\)), the image is \((5,-5)\) (the answer depends on the original point, this is just an example).