When reflecting a point across the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign.
Given the point at the bottom of the heart in the original figure is \((3 \frac{1}{4}, 7 \frac{1}{2})\), we first convert the mixed numbers to improper fractions:
- \(3 \frac{1}{4} = \frac{13}{4}\)
- \(7 \frac{1}{2} = \frac{15}{2}\)
Now, reflecting across the x-axis means we keep the x-coordinate the same and negate the y-coordinate. Thus:
- The x-coordinate remains \(\frac{13}{4}\).
- The y-coordinate becomes \(-\frac{15}{2}\).
So, the coordinates for the point at the bottom of the heart in the reflected image are:
\(\left( \frac{13}{4}, -\frac{15}{2} \right)\).
In decimal form, these coordinates can also be represented as:
\((3.25, -7.5)\).
Thus, the final answer is:
\(\left( \frac{13}{4}, -\frac{15}{2} \right)\) or in decimal form, \((3.25, -7.5)\).