To find the reflected coordinates of a point across the x-axis, you need to 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 as \((3 \frac{1}{4}, 7 \frac{1}{2})\). First, let's convert these mixed numbers into improper fractions:
- \(3 \frac{1}{4} = \frac{13}{4}\)
- \(7 \frac{1}{2} = \frac{15}{2}\)
Now the original point can be written as \(\left(\frac{13}{4}, \frac{15}{2}\right)\).
Next, we reflect this point across the x-axis by changing the sign of the y-coordinate:
The new coordinates will be: \[ \left(\frac{13}{4}, -\frac{15}{2}\right) \]
Thus, the coordinates for the point at the bottom of the heart in the reflected image are \(\left(\frac{13}{4}, -\frac{15}{2}\right)\).
If you would like this in a decimal format, it would look like:
- \(\frac{13}{4} = 3.25\)
- \(-\frac{15}{2} = -7.5\)
So the reflected coordinates can also be expressed as \((3.25, -7.5)\).
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