Question

A triangle was translated by a given RULE; the pre-image and image are given. Find the rule of translationI(-2,-3), W(-3,0), X(1,-2)toI'(-1,-5), W'(-2,-2), X'(2,-4)

Answer 1

The rule of translation for the given triangle is to add 1 to the x-coordinates and subtract 2 from the y-coordinates.

Step-by-step explanation:

To find the rule of translation, we need to determine how the $x$-coordinates and $y$-coordinates of the image points relate to the pre-image points. Let's examine the $x$-coordinates first:

The $x$-coordinate of the pre-image point $I$ is -2, and the $x$-coordinate of the image point $I'$ is -1.

This means that the $x$-coordinate increased by 1.

The $x$-coordinate of the pre-image point $W$ is -3, and the $x$-coordinate of the image point $W'$ is -2.

This also means that the $x$-coordinate increased by 1.

The $x$-coordinate of the pre-image point $X$ is 1, and the $x$-coordinate of the image point $X'$ is 2.

This means that the $x$-coordinate increased by 1.

From these observations, we can conclude that the translation rule for the $x$-coordinates is to add 1.

Now let's do the same for the $y$-coordinates:

The $y$-coordinate of the pre-image point $I$ is -3, and the $y$-coordinate of the image point $I'$ is -5.

This means that the $y$-coordinate decreased by 2.

The $y$-coordinate of the pre-image point $W$ is 0, and the $y$-coordinate of the image point $W'$ is -2.

This means that the $y$-coordinate decreased by 2.

The $y$-coordinate of the pre-image point $X$ is -2, and the $y$-coordinate of the image point $X'$ is -4.

This also means that the $y$-coordinate decreased by 2.

From these observations, we can conclude that the translation rule for the $y$-coordinates is to subtract 2.

Therefore, the rule of translation for this triangle is to add 1 to the $x$-coordinates and subtract 2 from the $y$-coordinates.