To reflect a point across the x-axis, the y-coordinate of the point changes its sign while the x-coordinate remains the same.
The original coordinates of the point at the bottom of the heart are given as \((3 \frac{1}{4}, 7 \frac{1}{2})\).
First, convert the mixed numbers to improper fractions:
- \(3 \frac{1}{4} = \frac{13}{4}\)
- \(7 \frac{1}{2} = \frac{15}{2}\)
Now, the coordinates are \((\frac{13}{4}, \frac{15}{2})\).
When reflecting this point across the x-axis, we change the sign of the y-coordinate:
\[ \text{Reflected Point} = \left( \frac{13}{4}, -\frac{15}{2} \right) \]
Thus, the coordinates for the point at the bottom of the heart in the reflected image are:
\[ \left( \frac{13}{4}, -\frac{15}{2} \right) \]
To express this in mixed number format:
- \( \frac{13}{4} = 3 \frac{1}{4} \) (as before)
- \(-\frac{15}{2} = -7 \frac{1}{2}\)
Therefore, the coordinates of the reflected point can also be written as:
\[ \left( 3 \frac{1}{4}, -7 \frac{1}{2} \right) \]
In conclusion, the coordinates for the point at the bottom of the heart in the reflected image are:
\(\left( \frac{13}{4}, -\frac{15}{2} \right)\) or \((3 \frac{1}{4}, -7 \frac{1}{2})\).