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?(1 point) ( , )

Answer 1

When a point is reflected across the x-axis, the x-coordinate remains the same, while the y-coordinate changes its sign.

Given the point at the bottom of the heart is \((3 \frac{1}{4}, 7 \frac{1}{2})\), we first convert the mixed numbers into improper fractions for easier calculation.

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

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

Now the original coordinates of the point are:
\[
\left(\frac{13}{4}, \frac{15}{2}\right)
\]

Next, we reflect this point across the x-axis. 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:
\[
\left(\frac{13}{4}, -\frac{15}{2}\right)
\]

In decimal form, this can also be expressed as approximately:
\((3.25, -7.5)\)

Final answer:
\[
\left(\frac{13}{4}, -\frac{15}{2}\right) \text{ or } (3.25, -7.5)
\]