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Triangle MNO is translated up 5 units and left 2 units. Point N is located at (0,6). What are the coordinates of N'? (1 point)

(-2,-11)

(-2,-1)

(2,-1)

(5,-8)

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 ¼,7 ½), what are the coordinates for the point at the bottom of the heart in the reflected image?

(Blank, blank)

1 answer

To find the new coordinates \( N' \) after translating Point \( N \) located at \( (0,6) \) up 5 units and left 2 units, we can perform the translation step by step:

  1. Translating up 5 units:

    • The y-coordinate increases by 5.
    • New coordinates after the upward translation are: \[ (0, 6 + 5) = (0, 11) \]

  2. Translating left 2 units:

    • The x-coordinate decreases by 2.
    • New coordinates after moving left are: \[ (0 - 2, 11) = (-2, 11) \]

So, the coordinates of \( N' \) are \( (-2, 11) \).

Now we need to reflect the point \( (3 \frac{1}{4}, 7 \frac{1}{2}) \) across the x-axis:

  • The reflection across the x-axis changes the sign of the y-coordinate, while the x-coordinate remains the same.

  1. Convert mixed numbers to improper fractions (or decimals) for easier calculations:

    • \( 3 \frac{1}{4} = \frac{13}{4} = 3.25 \)
    • \( 7 \frac{1}{2} = \frac{15}{2} = 7.5 \)

  2. Reflect the point:

    • The x-coordinate remains: \( 3.25 \)
    • The y-coordinate changes sign: from \( 7.5 \) to \( -7.5 \)

Thus, the coordinates of the point at the bottom of the heart in the reflected image are \( (3.25, -7.5) \).

So, the final answers are:

  1. For \( N' \): (-2, 11)
  2. For the reflected image: (3.25, -7.5)