Asked by burnout
Rotate the point (−4, −6)
on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses
(−6, −4)
left parenthesis negative 6 comma negative 4 right parenthesis
(6, −4)
left parenthesis 6 comma negative 4 right parenthesis
(6, 4)
left parenthesis 6 comma 4 right parenthesis
(−6, 4)
on a geometric figure 90 degrees counterclockwise. What is the new point?(1 point)
Responses
(−6, −4)
left parenthesis negative 6 comma negative 4 right parenthesis
(6, −4)
left parenthesis 6 comma negative 4 right parenthesis
(6, 4)
left parenthesis 6 comma 4 right parenthesis
(−6, 4)
Answers
Answered by
GPT-4o mini
To rotate the point \((-4, -6)\) 90 degrees counterclockwise, you can use the following formula for rotation:
If a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates \((x', y')\) will be:
\[
(x', y') = (-y, x)
\]
For the point \((-4, -6)\):
1. Identify \(x\) and \(y\): \(x = -4\), \(y = -6\)
2. Apply the rotation formula:
\[
x' = -y = -(-6) = 6
\]
\[
y' = x = -4
\]
So the new point after the rotation is \((6, -4)\).
The correct answer is \((6, -4)\).
If a point \((x, y)\) is rotated 90 degrees counterclockwise about the origin, the new coordinates \((x', y')\) will be:
\[
(x', y') = (-y, x)
\]
For the point \((-4, -6)\):
1. Identify \(x\) and \(y\): \(x = -4\), \(y = -6\)
2. Apply the rotation formula:
\[
x' = -y = -(-6) = 6
\]
\[
y' = x = -4
\]
So the new point after the rotation is \((6, -4)\).
The correct answer is \((6, -4)\).
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