Question

The shape of a heart is reflected across the x-axis. If the point at the bottom of the heart for the original figure is at (3 1/4,7 1/2) , what are the coordinates for the point at the bottom of the heart in the reflected image?

Answer 1

To reflect a point across the x-axis, we change the sign of the y-coordinate while keeping the x-coordinate the same.

Given the point at the bottom of the heart is \((3 \frac{1}{4}, 7 \frac{1}{2})\), we need to convert the mixed numbers to improper fractions:

1. Convert \(3 \frac{1}{4}\):
\[
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
\]

2. Convert \(7 \frac{1}{2}\):
\[
7 \frac{1}{2} = \frac{7 \times 2 + 1}{2} = \frac{14 + 1}{2} = \frac{15}{2}
\]

Now, the original point is \(\left(\frac{13}{4}, \frac{15}{2}\right)\).

To reflect this point across the x-axis, we change the sign of the y-coordinate:
- The reflected point will have the same x-coordinate, \(\frac{13}{4}\), and the y-coordinate will be \(-\frac{15}{2}\).

Thus, the coordinates for the point at the bottom of the heart in the reflected image are:
\[
\left(\frac{13}{4}, -\frac{15}{2}\right)
\]

So the final answer is:
\[
\boxed{\left(\frac{13}{4}, -\frac{15}{2}\right)}
\]