$$ riangle A B C $$ is dilated about the origin, resulting in $$ riangle X Y Z $$. Point $$ Z $$ is located at $$ (72,0) $$. What are the coordinates of point $$ X $$ ?

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$$ 	riangle A B C $$ is dilated about the origin, resulting in $$ 	riangle X Y Z $$. Point $$ Z $$ is located at $$ (72,0) $$. What are the coordinates of point $$ X $$ ?

UpStudy AI · Accepted Answer

To find the coordinates of point $$ X $$ after the dilation of triangle $$ ABC $$ to triangle $$ XYZ $$, we need to understand the relationship between the original triangle and the dilated triangle.

1. **Understanding Dilation**: Dilation about the origin means that each point of the triangle is moved away from or towards the origin by a certain scale factor $$ k $$. If a point $$ (x, y) $$ is dilated by a factor $$ k $$, its new coordinates become $$ (kx, ky) $$.

2. **Given Information**: We know that point $$ Z $$ is located at $$ (72, 0) $$. This means that the dilation has moved point $$ Z $$ to this position.

3. **Finding the Scale Factor**: To find the coordinates of point $$ X $$, we need to know the original coordinates of point $$ A $$ (or $$ B $$ or $$ C $$). However, since we don't have those coordinates, we can express the coordinates of point $$ X $$ in terms of the scale factor $$ k $$.

4. **Assuming Point $$ A $$**: Let's denote the original coordinates of point $$ A $$ as $$ (x_A, y_A) $$. After dilation, the coordinates of point $$ X $$ will be $$ (kx_A, ky_A) $$.

5. **Finding $$ k $$**: Since we know the coordinates of point $$ Z $$ after dilation, we can express the relationship:
   $$
   Z = (k \cdot x_Z, k \cdot y_Z) = (72, 0)
   $$
   If we assume the original coordinates of point $$ Z $$ were $$ (x_Z, y_Z) $$, we can find $$ k $$ if we know $$ (x_Z, y_Z) $$.

6. **Conclusion**: Without the original coordinates of point $$ A $$ or the scale factor $$ k $$, we cannot determine the exact coordinates of point $$ X $$. If you provide the original coordinates of point $$ A $$ or the scale factor $$ k $$, I can calculate the coordinates of point $$ X $$.

Please provide additional information to proceed.
Cannot determine the coordinates of point $$ X $$ with the given information.

is dilated about the origin, resulting in . Point is located at . What are the coordinates of point ?

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