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)
(
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, 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 \((3 \frac{1}{4}, -7 \frac{1}{2})\).