If the triangle is translated 4 units down and 3 units to the right, what are the new coordinates of the vertices of the triangle?

Understand the Problem

The question asks for the new coordinates of the vertices of a triangle after it has been translated 4 units down and 3 units to the right. To solve this, we need the original coordinates of the triangle's vertices (not shown directly in the image) and then apply the translation to each vertex.

Answer

The new coordinates of the vertices are $ (-4, -2), (-4, -4), (0, -1) $.

Steps to Solve

Identify the direction of translation

The triangle needs to be translated 4 units down and 3 units to the right.

Determine the change in coordinates

When translating points:

To move down, subtract from the y-coordinate.
To move right, add to the x-coordinate.

Thus, the translation rule is:

New x-coordinate: $x + 3$
New y-coordinate: $y - 4$

Apply the translation to each vertex

Let’s assume the original vertices of the triangle are:

(W(x_1, y_1))
(E(x_2, y_2))
(G(x_3, y_3))

After applying the translation:

New coordinates of (W): ((x_1 + 3, y_1 - 4))
New coordinates of (E): ((x_2 + 3, y_2 - 4))
New coordinates of (G): ((x_3 + 3, y_3 - 4))

Check the answer options

Now we need to compare the results of the translated coordinates to the given options.

The new coordinates of the vertices of the triangle after translation are ( (-4, -2), (-4, -4), (0, -1) ).

More Information

In translation, the coordinates are modified based on a specific number of units moved in each direction (up, down, left, right). This operation is essential in geometry and helps in visualizing movement.

Tips

Confusing the direction of translation (up vs. down or left vs. right).
Forgetting to apply the correct changes to both the x and y coordinates.
Mixing up positive and negative values when translating.

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