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

The original point at the bottom of the heart is given as \((3 \frac{1}{4}, 7 \frac{1}{2})\). First, let's convert these mixed numbers into improper fractions:

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

Now the original point can be written as \(\left(\frac{13}{4}, \frac{15}{2}\right)\).

Next, we reflect this point across the x-axis by changing the sign of the y-coordinate:

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

If you would like this in a decimal format, it would look like:
- \(\frac{13}{4} = 3.25\)
- \(-\frac{15}{2} = -7.5\)

So the reflected coordinates can also be expressed as \((3.25, -7.5)\).