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)

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1 answer

When reflecting a point 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 in the original figure is \((3 \frac{1}{4}, 7 \frac{1}{2})\), we first convert the mixed numbers to improper fractions:

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

Now, reflecting across the x-axis means we keep the x-coordinate the same and negate the y-coordinate. Thus:

  • The x-coordinate remains \(\frac{13}{4}\).
  • The y-coordinate becomes \(-\frac{15}{2}\).

So, 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, these coordinates can also be represented as:

\((3.25, -7.5)\).

Thus, the final answer is:

\(\left( \frac{13}{4}, -\frac{15}{2} \right)\) or in decimal form, \((3.25, -7.5)\).