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

First, let's convert these mixed numbers to improper fractions:

• \(3 \frac{1}{4} = \frac{13}{4}\)
• \(7 \frac{1}{2} = \frac{15}{2}\)

Now 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 point at the bottom of the heart in the reflected image are:

\[ \left(\frac{13}{4}, -\frac{15}{2}\right) \]

If you prefer to express these as mixed numbers:

• \(\frac{13}{4} = 3 \frac{1}{4}\)
• \(-\frac{15}{2} = -7 \frac{1}{2}\)

So the reflected point is \( \left(3 \frac{1}{4}, -7 \frac{1}{2}\right) \).