Rotate a point on a line at (−4, 6)

Question

180°
counterclockwise. What is the resulting point?(1 point)
Responses

(4, −6)
left parenthesis 4 comma negative 6 right parenthesis

(−4, −6)
left parenthesis negative 4 comma negative 6 right parenthesis

(−6, 4)
left parenthesis negative 6 comma 4 right parenthesis

(6, −4)
left parenthesis 6 comma negative 4 right parenthesis

Answer 1

To rotate a point 180° counterclockwise around another point, you can use the following steps:

1. Determine the coordinates of the original point, which is (-4, 6), and the point of rotation, which is also (-4, 6) in this case.
2. The formula for a 180° rotation around a point (a, b) is: \[ (x', y') = (2a - x, 2b - y) \]

In this case, since the point of rotation and the original point are the same (both (-4, 6)), we can plug in these values:

• a = -4
• b = 6
• x = -4
• y = 6

Using the formula: \[ x' = 2(-4) - (-4) = -8 + 4 = -4 \] \[ y' = 2(6) - 6 = 12 - 6 = 6 \]

This result means that rotating (-4, 6) by 180° around (-4, 6) results in the same point (-4, 6).

However, if we think of rotating about the origin (0, 0), we would instead check:

\[ x' = -(-4) = 4, \] \[ y' = -6 = -6. \]

Again, since we aren't rotating around the origin here, we won't use that.

Let's summarize:

• The result of rotating (-4, 6) by 180° around itself is (-4, 6).

However, if the question implies a different point, assuming the question was to just rotate around the origin (-4, 6), the likelihood of selection can point us towards another point generally:

If rotating around another option is preferred, we consider:

• Rotating point (−4, 6) 180° around (0, 0) results in (4, −6).

So the best guess here would be: (4, −6) or (0,0) else this case is redundant.

Thus the answer would be (4, −6).