To reflect a point across the x-axis, you change the sign of the y-coordinate while keeping the x-coordinate the same.
The original point at the bottom of the heart is given in mixed fractions as \( (3 \frac{1}{4}, 7 \frac{1}{2}) \).
First, we need to convert these mixed fractions to improper fractions or decimal form:
- \( 3 \frac{1}{4} = \frac{13}{4} \) or \( 3.25 \)
- \( 7 \frac{1}{2} = \frac{15}{2} \) or \( 7.5 \)
Now we will reflect the point \( (\frac{13}{4}, \frac{15}{2}) \) across the x-axis:
- The x-coordinate remains \( \frac{13}{4} \).
- The y-coordinate changes from \( \frac{15}{2} \) to \( -\frac{15}{2} \).
Thus, the coordinates for the reflected image of the point at the bottom of the heart will be:
\[ \left( \frac{13}{4}, -\frac{15}{2} \right) \]
Therefore, the final answer is:
\(( \frac{13}{4}, -\frac{15}{2} )\)