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

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

Given the point at the bottom of the heart is \((3\frac{1}{4}, 7\frac{1}{2})\), we first convert these mixed numbers to improper fractions:

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

So the point can be expressed as \(\left(\frac{13}{4}, \frac{15}{2}\right)\).

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

• The reflection of this point 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 \(\left(\frac{13}{4}, -\frac{15}{2}\right)\).