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 find the coordinates of the point after reflecting across the x-axis, you need to change the sign of the y-coordinate while keeping the x-coordinate the same.

The original point given is \( (3 \frac{1}{4}, 7 \frac{1}{2}) \).

First, convert the mixed numbers into improper fractions or decimals:

- \( 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \)
- \( 7 \frac{1}{2} = 7 + \frac{1}{2} = 7 + 0.5 = 7.5 = \frac{15}{2} \)

So the coordinates are \( \left(\frac{13}{4}, \frac{15}{2}\right) \).

Now, reflecting this point across the x-axis involves changing the y-coordinate:

1. The x-coordinate remains the same: \( \frac{13}{4} \).
2. The y-coordinate changes sign: \( -\frac{15}{2} \).

Thus, the reflected point's coordinates are:

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

So the coordinates for the point at the bottom of the heart in the reflected image are \( \left(3 \frac{1}{4}, -7 \frac{1}{2}\right) \).